Finite Group Databasebeta

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C₇×(C₇⋊C₉)⋊Dic₁₃ #37524330

order	22932
automorphism	?
homology	Abelianization (H₁) = C₄×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×(C₇⋊C₉)⋊Dic₁₃
unambiguous semidirect product	(C₇⋊C₉)⋊(C₇×Dic₁₃)

Splittings

derived	C₇×C₁₃ ⋊ C₄×C₇×C₉
Hall	C₇×C₁₃×C₇⋊C₉ ⋊ C₄
Hall	C₇×Dic₉₁ ⋊ C₉
Hall	C₇²×C₁₃ ⋊ C₄×C₉
Hall	C₇×C₇⋊C₉ ⋊ Dic₁₃
Sylow	C₇² ⋊ C₉×Dic₁₃
Sylow	C₁₃ ⋊ C₇×Dic₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	ΓL(1,𝔽₈)⋊D₁₃
commutator, hypocenter	C₇×C₁₃	C₄×C₇×C₉
Frattini	C₂×C₃	C₇×ΓL(1,𝔽₈)⋊D₁₃
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₃	C₂×C₃
cosocle	C₂×C₃×C₇×C₁₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₃×C₇

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3276

Conjugacy classes & character table

1554 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 275);