C₂²×C₃×D₃×C₅⋊D₅ #72229693

order	3600
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶×C₅

Aliases

C₂²×C₃×D₃×C₅⋊D₅

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₃×C₅⋊D₅
commutator, cosocle, hypocenter	C₃×C₅²	C₂⁴×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₅²	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂²×C₃

2272 conjugacy classes of subgroups; only the 460 normal subgroups are shown.

normal subgroups only

This group has 2272 conjugacy classes of subgroups — too many to draw. Only its 460 normal subgroups are shown.

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

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 600

A minimal faithful permutation representation — 4 generators on 20 points:

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

504 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((1,2,3)(4,5,6)(12,13,15,16,14)(19,20), (8,9)(10,11)(13,14)(15,16), (7,8,10,11,9)(17,18), (5,6));