D₄×#92259 #72229329

order	3888
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃

Aliases

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

1194 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 72

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

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

maximal subgroup of	D₄×#13091119, D₄×(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃
maximal normal subgroup of	D₄×(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃

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

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