D₈×#1020 #72258747

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂⁴×D₈ ⋊ D₃

3997 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 3997 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 16 points:

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

maximal subgroup of	AGL(1,ℤ/8)×#1020, D₈×A₄⋊S₄
maximal normal subgroup of	AGL(1,ℤ/8)×#1020

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

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