REPORTABLE SEGMENTS (Details) - Schedule of summary of reconciliation of segment profit before taxes and operations - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Segment Reporting Information [Line Items]
Revenue	$ 660,673	$ 632,061	$ 566,350	$ 548,438	$ 574,164	$ 574,970	$ 549,633	$ 510,522	$ 2,407,522	$ 2,209,289	$ 1,977,918
Segment Adjusted EBITDA									282,912	245,942	213,463
Unallocated amounts, excluding depreciation									(47,013)	(46,302)	(45,343)
Adjusted EBITDA									235,899	199,640	168,120
Net interest expense									(65,791)	(67,260)	(63,871)
Depreciation and amortization									(62,409)	(61,848)	(55,803)
Restructuring charges									(15,790)	0	0
Loss from debt extinguishment		$ (969)	$ (5,245)						(7,925)	0	0
Acquisition contingent consideration	$ (1,403)				$ 1,333				1,733	1,646	0
Acquisition costs									(2,960)	0	(7,597)
Special dividend charges											(2,588)
Secondary equity offering costs									0	0	(1,205)
Income before taxes from continuing operations									82,757	72,178	33,810
Capital expenditures									48,998	45,361	50,138
Consumer and Professional Products
Segment Reporting Information [Line Items]
Revenue									1,139,233	1,000,608	953,612
Segment Adjusted EBITDA									104,053	90,677	77,061
Depreciation and amortization									(32,788)	(32,289)	(30,816)
Capital expenditures									23,321	17,828	23,040
Home and Building Products (HBP)
Segment Reporting Information [Line Items]
Revenue									927,313	873,640	697,969
Segment Adjusted EBITDA									153,631	120,161	100,339
Depreciation and amortization									(18,361)	(18,334)	(13,717)
Capital expenditures									17,499	16,498	13,547
Defense Electronics
Segment Reporting Information [Line Items]
Revenue									340,976	335,041	326,337
Segment Adjusted EBITDA									25,228	35,104	36,063
Depreciation and amortization									(10,645)	(10,667)	(10,801)
Capital expenditures									7,830	10,492	10,941
Operating
Segment Reporting Information [Line Items]
Depreciation and amortization									(61,794)	(61,290)	(55,334)
Capital expenditures									48,650	44,818	47,528
Corporate
Segment Reporting Information [Line Items]
Depreciation and amortization									(615)	(558)	(469)
Capital expenditures									348	543	2,610
Continuing Operations
Segment Reporting Information [Line Items]
Special dividend charges									0	0	(3,220)
Postretirement Life Insurance | Continuing Operations
Segment Reporting Information [Line Items]
Cost of life insurance benefit									$ 0	$ 0	$ (2,614)