C₄×#1386 #146339

order	512
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₄³ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

736 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4);(5,6,7,8)(9,10,13,17)(11,12,19,21)(14,16,22,24)(15,23,20,18);(9,11,14,18,15,16,21,17,13,19,22,23,20,24,12,10)

maximal subgroup of	#72214203, C₄×#12647, #72216468, …
maximal normal subgroup of	#72214203, C₄×#12647, #72216468, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 53535);