Finite Group Databasebeta

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C₁₀₇×D₁₃⋊C₉ #38736693

order	25038
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₀₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₀₇×D₁₃⋊C₉
unambiguous semidirect product	D₁₃⋊(C₉×C₁₀₇)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₂×C₁₀₇)
unambiguous semidirect product	(D₁₃×C₁₀₇)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₁₀₇
Hall	C₁₀₇×C₁₃⋊C₉ ⋊ C₂
Hall	D₁₃×C₁₀₇ ⋊ C₉
Hall	C₁₃×C₁₀₇ ⋊ C₂×C₉
Hall	C₁₃⋊C₉ ⋊ C₂×C₁₀₇
Hall	D₁₃ ⋊ C₉×C₁₀₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₀₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₉×C₁₀₇
Frattini	C₃	D₁₃⋊C₃×C₁₀₇
Fitting, socle	C₃×C₁₃×C₁₀₇	C₂×C₃
prime radical	C₃×D₁₃×C₁₀₇	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₁₀₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₀₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12519

Conjugacy classes & character table

2568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25038, 11);