C₄×#101 #1756

order	128
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	Aut(G) = #72237495 (order 4096) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂²×B(4,𝔽₂)
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

148 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 488);