C₂×#358 #2137

order	128
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	Aut(G) order 4096
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

116 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 869);