Finite Group Databasebeta

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C₁₃×C₂₉×C₇⋊C₉ #37557646

order	23751
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₂₉×C₇⋊C₉
unambiguous semidirect product	C₇⋊(C₉×C₁₃×C₂₉)
unambiguous semidirect product	(C₇×C₂₉)⋊(C₉×C₁₃)

Splittings

derived, Sylow	C₇ ⋊ C₉×C₁₃×C₂₉
Hall	C₇×C₁₃×C₂₉ ⋊ C₉
Hall	C₇×C₂₉ ⋊ C₉×C₁₃
Hall	C₇×C₁₃ ⋊ C₉×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₂₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₉×C₁₃×C₂₉
Frattini	C₃	C₁₃×ΓL(1,𝔽₈)×C₂₉
Fitting, socle, prime radical	C₃×C₇×C₁₃×C₂₉	C₃
cosocle	C₃×C₇	C₃×C₁₃×C₂₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₃×C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 23751

Conjugacy classes & character table

5655 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23751, 4);