Finite Group Databasebeta

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C₇×C₂₃×C₁₃⋊C₉ #34038076

order	18837
automorphism	?
homology	Abelianization (H₁) = C₇×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₂₃×C₁₃⋊C₉
unambiguous semidirect product	C₁₃⋊(C₇×C₉×C₂₃)
unambiguous semidirect product	(C₁₃×C₂₃)⋊(C₇×C₉)

Splittings

derived, Sylow	C₁₃ ⋊ C₇×C₉×C₂₃
Hall	C₇×C₁₃×C₂₃ ⋊ C₉
Hall	C₁₃×C₂₃ ⋊ C₇×C₉
Hall	C₇×C₁₃ ⋊ C₉×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇×C₂₃	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₇×C₉×C₂₃
Frattini	C₃	C₇×C₂₃×C₁₃⋊C₃
Fitting, socle, prime radical	C₃×C₇×C₁₃×C₂₃	C₃
cosocle	C₃×C₁₃	C₃×C₇×C₂₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇×C₂₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18837

Conjugacy classes & character table

3381 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇×C₂₃×C₁₃⋊C₉, C₇×D₂₃×C₁₃⋊C₉, C₇×C₂₃×D₁₃⋊C₉, …
maximal normal subgroup of	C₂×C₇×C₂₃×C₁₃⋊C₉, C₇×D₂₃×C₁₃⋊C₉, C₇×C₂₃×D₁₃⋊C₉, …
maximal quotient of	C₂×C₇×C₂₃×C₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18837, 2);