D₄×#4169⋊C₃ #72229352

order	3888
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃²

Aliases

Fitting	D₄×#6891 ⋊ C₂
Sylow	#6891 ⋊ C₂×D₄

1516 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 22 points:

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

maximal subgroup of	D₄×(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃, D₄×(#4169⋊C₃)⋊C₃
maximal normal subgroup of	D₄×(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃, D₄×(#4169⋊C₃)⋊C₃

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

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