C₄×#3092 #6373049

order	512
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

2880 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 20 points:

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

maximal subgroup of	#72283561, #72283649
maximal normal subgroup of	#72283561, #72283649

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280245);