C₂³×#1896 #72308180

order	1024
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁶

Aliases

98589 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 6 generators on 18 points:

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

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

maximal subgroup of	C₂³×#21546
maximal normal subgroup of	C₂³×#21546

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

gap> G := Group((12,15,16,17), (1,2), (3,4), (1,2)(3,4)(5,6)(7,8)(9,10), (5,6), (7,9,10,8)(11,12)(13,17)(14,16)(15,18));