C₂⁴×#388 #72325617

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₄ · Schur multiplier (H₂) = C₂²⁰×C₄

Aliases

C₂⁴×#388

306485 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 7 generators on 20 points:

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

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

maximal subgroup of	C₂³×#15159, C₂³×#14796, C₂⁴×#2684, …
maximal normal subgroup of	C₂³×#15159, C₂³×#14796, C₂⁴×#2684, …

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

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