C₂³×#1383 #72307661

order	1024
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂¹¹

Aliases

14213 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(12,16,17,22)(13,19)(14,21)(18,25,24,23)(20,26);(7,8,9,10)(11,12,13,16,14,18,19,23,15,17,20,22,21,24,26,25);(3,4);(5,6)

maximal subgroup of	C₂³×#12647, C₂³×#13037, C₂³×#12929
maximal normal subgroup of	C₂³×#12647, C₂³×#13037, C₂³×#12929

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

gap> G := Group((1,2), (12,16,17,22)(13,19)(14,21)(18,25,24,23)(20,26), (7,8,9,10)(11,12,13,16,14,18,19,23,15,17,20,22,21,24,26,25), (3,4), (5,6));