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C₅×C₉×C₁₃×D₁₁ #27166011

order	12870
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₅×C₉×C₁₃×D₁₁

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉×C₁₃	D₁₁
commutator, hypocenter	C₁₁	C₂×C₅×C₉×C₁₃
Frattini	C₃	C₃×C₅×C₁₃×D₁₁
Fitting	C₅×C₉×C₁₁×C₁₃	C₂
socle	C₃×C₅×C₁₁×C₁₃	C₂×C₃
prime radical	C₃×C₅×C₁₃×D₁₁	C₃
cosocle	C₃×C₁₁	C₂×C₃×C₅×C₁₃
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅×C₉×C₁₃

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 6435

A minimal faithful permutation representation — 2 generators on 38 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24)(25,26,28,27,29,31,30,32,33)(34,35,36,37,38);(1,2,4,6,8,10,11,9,7,5,3)

Conjugacy classes & character table

4095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×D₁₁×D₁₃, C₉×D₅×C₁₃×D₁₁, C₉×D₁₁×D₆₅, …
maximal normal subgroup of	C₅×C₉×D₁₁×D₁₃, C₉×D₅×C₁₃×D₁₁, C₉×D₁₁×D₆₅, …
maximal quotient of	C₅×C₉×C₁₃×Dic₁₁, C₂×C₅×C₉×C₁₃×D₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 6);