Finite Group Databasebeta

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C₁₃×D₂₃₇ #20259705

order	6162
isoclinism	isoclinic class of D₂₃₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₂₃₇
unambiguous semidirect product	C₃⋊(C₁₃×D₇₉)

Splittings

Fitting, socle, Hall	C₃×C₁₃×C₇₉ ⋊ C₂
derived, Hall	C₃×C₇₉ ⋊ C₂×C₁₃
Hall	C₁₃×C₇₉ ⋊ D₃
Sylow	C₇₉ ⋊ D₃×C₁₃
Hall	C₃×C₁₃ ⋊ D₇₉
Sylow	C₃ ⋊ C₁₃×D₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₂₃₇
commutator, hypocenter	C₃×C₇₉	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₇₉	C₂
LCS	G ▷ C₃×C₇₉
UCS	C₁ ◁ C₁₃

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×C₁₃×D₇₉, D₁₃×D₂₃₇, D₃₉⋊D₇₉, …
maximal normal subgroup of	D₃×C₁₃×D₇₉, D₁₃×D₂₃₇, D₃₉⋊D₇₉, …
maximal quotient of	C₁₃×Dic₂₃₇, C₂×C₁₃×D₂₃₇, C₁₃×D₇₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6162, 12);