Finite Group Databasebeta

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C₂×C₁₃×C₃₁⋊C₉ #20299808

order	7254
isoclinism	isoclinic class of C₃₁⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₃×C₃₁⋊C₉
unambiguous semidirect product	(C₂×C₃₁)⋊(C₉×C₁₃)

Splittings

derived, Sylow	C₃₁ ⋊ C₂×C₉×C₁₃
Hall	C₂×C₁₃×C₃₁ ⋊ C₉
Hall	C₁₃×C₃₁ ⋊ C₂×C₉
Hall	C₂×C₃₁ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₂×C₉×C₁₃
Frattini	C₃	C₂×C₁₃×C₃₁⋊C₃
Fitting, socle	C₂×C₃×C₁₃×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1014 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×C₁₃×C₃₁⋊C₉, C₁₃×Dic₃₁⋊C₉, Dic₁₃×C₃₁⋊C₉, …
maximal normal subgroup of	C₄×C₁₃×C₃₁⋊C₉, C₁₃×Dic₃₁⋊C₉, Dic₁₃×C₃₁⋊C₉, …
maximal quotient of	C₄×C₁₃×C₃₁⋊C₉, C₂²×C₁₃×C₃₁⋊C₉, C₂×C₅×C₁₃×C₃₁⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7254, 2);