C₄×#10597113 #72229642

order	2400
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄×C₅

Aliases

864 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.

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

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 1200

A minimal faithful permutation representation — 3 generators on 21 points:

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

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

maximal subgroup of	C₄²×D₃×C₅⋊D₅, #72231116, #72260143
maximal normal subgroup of	C₄²×D₃×C₅⋊D₅, #72231116, #72260143

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

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