C₄×#1505 #182615

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

Aliases

1590 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)(8,10)(9,12)(14,17,18,19);(6,10)(7,8)(11,12)(13,14)(15,19)(16,18)(17,20);(5,7,9,8)(6,11,12,10)

maximal subgroup of	#72239593, #72239731
maximal normal subgroup of	#72239593, #72239731

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89811);