C₄×#1507 #182613

order	512
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

2052 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 20 points:

(1,2,3,4);(5,6)(7,11,12,9)(8,10)(13,14)(15,19)(16,18)(17,20);(5,7)(6,9)(8,12)(10,11)(14,18)(15,16)(19,20);(7,12)(9,11)(13,15,17,16)(14,19,20,18)

maximal subgroup of	#72309174, #72309181, #72309237, …
maximal normal subgroup of	#72309174, #72309181, #72309237, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89809);