C₄×#544 #34097

order	256
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	Aut(G) order 262144
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

1105 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)(7,11)(8,10)(9,12)(13,14,16,18)(15,19,20,17);(5,7,8,12)(6,9,10,11);(7,12)(9,11)(13,15,16,20)(14,17,18,19);(6,10)(9,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27085);