C₂×#2283 #34009

order	256
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 4194304
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

1623 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 5 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26997);