Finite Group Databasebeta

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C₉×D₇×C₁₃₁ #30658201

order	16506
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃₁ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₁₃₁

Splittings

Fitting, Hall	C₇×C₉×C₁₃₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₁₃₁
Hall	C₇×C₁₃₁ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₁₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₃₁	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₃₁
Frattini	C₃	C₃×D₇×C₁₃₁
Fitting	C₇×C₉×C₁₃₁	C₂
socle	C₃×C₇×C₁₃₁	C₂×C₃
prime radical	C₃×D₇×C₁₃₁	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₃₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₃₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8253

Conjugacy classes & character table

5895 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₃₁, D₇×D₉×C₁₃₁, D₇×D₁₁₇₉, …
maximal normal subgroup of	C₉×D₇×D₁₃₁, D₇×D₉×C₁₃₁, D₇×D₁₁₇₉, …
maximal quotient of	C₉×Dic₇×C₁₃₁, C₂×C₉×D₇×C₁₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16506, 4);