C₂×#1876 #20916

order	256
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

877 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13904);