C₂²×D₄×#127 #72258175

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂²⁰×C₄

Aliases

C₂²×D₄×#127

	subgroup	G/H
center, socle	C₂⁵	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁷
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ G
LECS	G ▷ C₂³ ▷ C₁

254013 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 7 generators on 16 points:

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

280 conjugacy classes. The character table is too large to display.

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((6,8), (10,12)(14,15), (3,4), (1,2)(3,4), (13,14,16,15), (9,10,11,12)(13,15,16,14), (5,6,7,8));