C₂×#383 #2282

order	128
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 393216
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

312 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1014);