Finite Group Databasebeta

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C₂×C₃₁×C₁₃⋊C₉ #20299809

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

Aliases

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

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1302 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7254, 3);