C₂×C₄×C₃⋊D₃×C₅⋊D₅ #72229789

order	7200
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₃×C₅

Aliases

5664 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 22 points:

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

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

maximal subgroup of	C₂×C₄×C₃⋊D₃×#1043, C₂×D₄×C₃⋊D₃×C₅⋊D₅, C₂×C₃⋊D₃×C₄⋊#1043
maximal normal subgroup of	C₂×C₄×C₃⋊D₃×#1043, C₂×D₄×C₃⋊D₃×C₅⋊D₅, C₂×C₃⋊D₃×C₄⋊#1043

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

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