C₂×C₃×D₄×C₅⋊D₅ #72229409

order	2400
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶×C₅

Aliases

C₂×C₃×D₄×C₅⋊D₅

1888 conjugacy classes of subgroups; only the 422 normal subgroups are shown.

normal subgroups only

This group has 1888 conjugacy classes of subgroups — too many to draw. Only its 422 normal subgroups are shown.

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

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 600

A minimal faithful permutation representation — 4 generators on 19 points:

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

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

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

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