Finite Group Databasebeta

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C₁₃×D₇×C₃₁ #19150677

order	5642
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₇×C₃₁
unambiguous semidirect product	C₇⋊(C₂×C₁₃×C₃₁)

Splittings

Fitting, socle, Hall	C₇×C₁₃×C₃₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₁₃×C₃₁
Hall	C₇×C₃₁ ⋊ C₂×C₁₃
Hall	C₇×C₁₃ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₃₁	D₇
commutator, hypocenter	C₇	C₂×C₁₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₃₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₃×C₃₁

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2015 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃×D₇×D₃₁, D₇×D₁₃×C₃₁, D₇×D₄₀₃, …
maximal normal subgroup of	C₁₃×D₇×D₃₁, D₇×D₁₃×C₃₁, D₇×D₄₀₃, …
maximal quotient of	C₁₃×Dic₇×C₃₁, C₂×C₁₃×D₇×C₃₁, C₃×C₁₃×D₇×C₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5642, 5);