C₂×C₃⋊Dic₃×C₅⋊D₅ #72229776

order	3600
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³×C₃×C₅

Aliases

1296 conjugacy classes of subgroups; only the 338 normal subgroups are shown.

normal subgroups only

This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 338 normal subgroups are shown.

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

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

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

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

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

maximal subgroup of	C₂×C₄×C₃⋊D₃×C₅⋊D₅, C₂×C₃⋊Dic₃×#1043, C₂×C₅⋊D₅×#638, …
maximal normal subgroup of	C₂×C₄×C₃⋊D₃×C₅⋊D₅, C₂×C₃⋊Dic₃×#1043, C₂×C₅⋊D₅×#638, …

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

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