C₄×#534 #34087

order	256
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	Aut(G) order 262144
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

1885 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 5 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27075);