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C₉×C₁₃²⋊C₇ #24922392

order	10647
automorphism	?
homology	Abelianization (H₁) = C₇×C₉ · Schur multiplier (H₂) = C₁₃

Aliases

direct product	C₉×C₁₃²⋊C₇
unambiguous semidirect product	(C₉×C₁₃²)⋊C₇

Splittings

Fitting, Hall	C₉×C₁₃² ⋊ C₇
derived, Sylow	C₁₃² ⋊ C₇×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₁₃²⋊C₇
commutator, hypocenter	C₁₃²	C₇×C₉
Frattini	C₃	C₃×C₁₃²⋊C₇
Fitting	C₉×C₁₃²	C₇
socle, cosocle	C₃×C₁₃²	C₃×C₇
prime radical	C₃×C₁₃²⋊C₇	C₃
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₉

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

279 conjugacy classes — view the full character table.

Relationships

derived subgroup of	C₉⋊#14556975
maximal subgroup of	C₉×#14556975, C₉×(C₁₃⋊D₁₃)⋊C₇, C₉⋊#14556975, …
maximal normal subgroup of	C₉×#14556975, C₉×(C₁₃⋊D₁₃)⋊C₇, C₉⋊#14556975, …
maximal quotient of	C₂×C₉×C₁₃²⋊C₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10647, 14);