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C₉×D₁₃×C₇⋊D₇ #37524563

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₇

Aliases

C₉×D₁₃×C₇⋊D₇

Splittings

Fitting, Hall	C₇²×C₉×C₁₃ ⋊ C₂²
derived, Hall	C₇²×C₁₃ ⋊ C₂²×C₉
Hall	C₇²×C₉ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×C₇⋊D₇
Sylow	C₇² ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₉×C₇⋊D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₃×C₇⋊D₇
commutator, hypocenter	C₇²×C₁₃	C₂²×C₉
Frattini	C₃	C₃×D₁₃×C₇⋊D₇
Fitting	C₇²×C₉×C₁₃	C₂²
socle, cosocle	C₃×C₇²×C₁₃	C₂²×C₃
prime radical	C₃×D₁₃×C₇⋊D₇	C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₉

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5733

Conjugacy classes & character table

1872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 508);