C₂×#424 #2904

order	128
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

256 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)(7,8,10,13,11,14,17,20)(9,12,16,19,15,18,21,22);(3,4,5,6)(7,9)(8,12)(10,16)(11,15)(13,19)(14,18)(17,21)(20,22);(9,15)(12,18)(16,21)(19,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1636);