C₂×C₃²×C₄×#1043 #72229751

order	7200
isoclinism	isoclinic class of #1043
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄² · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

C₂×C₃²×C₄×#1043

2592 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 1800

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

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

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

maximal subgroup of	C₂×C₄×C₃⋊D₃×#1043, C₂×C₃²×D₄×#1043, C₂×C₄⋊(C₃⋊D₃)×#1043, …
maximal normal subgroup of	C₂×C₄×C₃⋊D₃×#1043, C₂×C₃²×D₄×#1043, C₂×C₄⋊(C₃⋊D₃)×#1043, …

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

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