C₄×#2920 #6369955

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁶×C₄²

Aliases

3646 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)(13,14,15,18,16,17,19,20);(6,9)(10,12);(5,7,8,11)(6,10,9,12);(14,17)(18,20)

maximal subgroup of	#72239192, #72239229, #72239262, …
maximal normal subgroup of	#72239192, #72239229, #72239262, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277151);