C₁₁×D₇×C₃⋊(C₅⋊D₅) #37528702

order	23100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₁₁×D₇×C₃⋊(C₅⋊D₅)
unambiguous semidirect product	(C₃×D₇)⋊(C₁₁×C₅⋊D₅)
unambiguous semidirect product	(C₅×D₇)⋊(C₁₁×D₁₅)

	subgroup	G/H
center, hypercenter	C₁₁	D₇×C₃⋊(C₅⋊D₅)
commutator, cosocle, hypocenter	C₃×C₅²×C₇	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₁	C₂²
LCS	G ▷ C₃×C₅²×C₇
UCS	C₁ ◁ C₁₁

320 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

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

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 5775

A minimal faithful permutation representation — 3 generators on 31 points:

(2,3)(4,5,7,9,10,8,6)(12,13)(14,15)(17,18)(19,20)(21,22,23,24,25,26,27,28,29,30,31);(1,2,3)(5,6)(7,8)(9,10)(16,17,19,20,18);(11,12,14,15,13)

2145 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 513);