D₄×A₄×3₋¹⁺² #72253039

order	2592
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃³ · Schur multiplier (H₂) = C₂²×C₃²

Aliases

D₄×A₄×3₋¹⁺²

Fitting	C₂²×D₄×3₋¹⁺² ⋊ C₃
Sylow	C₂²×D₄ ⋊ C₃×3₋¹⁺²

880 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.

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

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 17 points:

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

maximal subgroup of	D₄×A₄⋊AGL(1,ℤ/9)
maximal normal subgroup of	D₄×A₄⋊AGL(1,ℤ/9)

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

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