Finite Group Databasebeta

← Prev (#37557644) Next (#37557646) →

C₇×C₂₉×C₁₃⋊C₉ #37557645

order	23751
automorphism	?
homology	Abelianization (H₁) = C₇×C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 23751

Conjugacy classes & character table

4263 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23751, 3);