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C₉×C₁₃×Dic₅ #14556703

order	2340
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₃×Dic₅

Splittings

derived, Sylow	C₅ ⋊ C₄×C₉×C₁₃
Hall	C₅×C₉×C₁₃ ⋊ C₄
Hall	C₅×C₁₃ ⋊ C₄×C₉
Hall	C₅×C₉ ⋊ C₄×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₃	D₅
commutator, hypocenter	C₅	C₄×C₉×C₁₃
Frattini	C₂×C₃	C₃×D₅×C₁₃
Fitting	C₂×C₅×C₉×C₁₃	C₂
socle, prime radical	C₂×C₃×C₅×C₁₃	C₂×C₃
cosocle	C₂×C₃×C₅	C₂×C₃×C₁₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₉×C₁₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 2340

A minimal faithful permutation representation — 2 generators on 31 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×C₁₃×Dic₂₅, C₅×C₉×C₁₃×Dic₅, C₉×C₁₃×#1039, …
maximal normal subgroup of	C₅×C₉×C₁₃×Dic₅, C₇×C₉×C₁₃×Dic₅, C₉×C₁₁×C₁₃×Dic₅, …
maximal quotient of	C₉×C₁₃×Dic₂₅, C₅×C₉×C₁₃×Dic₅, C₉×C₁₃×#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2340, 7);