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C₁₇×C₇₉⋊C₉ #27130613

order	12087
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₇₉⋊C₉
unambiguous semidirect product	C₇₉⋊(C₉×C₁₇)
unambiguous semidirect product	(C₁₇×C₇₉)⋊C₉

Splittings

derived, Sylow	C₇₉ ⋊ C₉×C₁₇
Hall	C₁₇×C₇₉ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₇₉⋊C₃
commutator, hypocenter	C₇₉	C₉×C₁₇
Frattini	C₃	C₁₇×C₇₉⋊C₃
Fitting, socle, prime radical	C₃×C₁₇×C₇₉	C₃
cosocle	C₃×C₇₉	C₃×C₁₇
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₃×C₁₇

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1479 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₇×C₇₉⋊C₉, C₁₇×D₇₉⋊C₉, D₁₇×C₇₉⋊C₉, …
maximal normal subgroup of	C₂×C₁₇×C₇₉⋊C₉, C₁₇×D₇₉⋊C₉, D₁₇×C₇₉⋊C₉, …
maximal quotient of	C₂×C₁₇×C₇₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12087, 2);