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C₇×C₁₆₉⋊C₉ #24922381

order	10647
automorphism	?
homology	Abelianization (H₁) = C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₆₉⋊C₉
unambiguous semidirect product	C₁₆₉⋊(C₇×C₉)

Splittings

derived, Sylow	C₁₆₉ ⋊ C₇×C₉
Hall	C₇×C₁₆₉ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	C₁₆₉⋊C₃
commutator, hypocenter	C₁₆₉	C₇×C₉
Frattini	C₃×C₁₃	C₇×C₁₃⋊C₃
Fitting	C₃×C₇×C₁₆₉	C₃
socle, prime radical	C₃×C₇×C₁₃	C₁₃⋊C₃
cosocle	C₃×C₁₆₉	C₃×C₇
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₃×C₇

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1239 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₁₆₉⋊C₉, D₇×C₁₆₉⋊C₉, (C₁₆₉⋊C₉)⋊D₇, …
maximal normal subgroup of	C₇×D₁₆₉⋊C₉, D₇×C₁₆₉⋊C₉, (C₁₆₉⋊C₉)⋊D₇, …
maximal quotient of	C₂×C₇×C₁₆₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10647, 3);