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C₁₇×C₄₃⋊C₉ #20267183

order	6579
isoclinism	isoclinic class of C₄₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₄₃⋊C₉
unambiguous semidirect product	C₄₃⋊(C₉×C₁₇)
unambiguous semidirect product	(C₁₇×C₄₃)⋊C₉

Splittings

derived, Sylow	C₄₃ ⋊ C₉×C₁₇
Hall	C₁₇×C₄₃ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₄₃⋊C₃
commutator, hypocenter	C₄₃	C₉×C₁₇
Frattini	C₃	C₁₇×C₄₃⋊C₃
Fitting, socle	C₃×C₁₇×C₄₃	C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×C₁₇

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

867 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₇×C₄₃⋊C₉, C₁₇×D₄₃⋊C₉, D₁₇×C₄₃⋊C₉, …
maximal normal subgroup of	C₂×C₁₇×C₄₃⋊C₉, C₁₇×D₄₃⋊C₉, D₁₇×C₄₃⋊C₉, …
maximal quotient of	C₂×C₁₇×C₄₃⋊C₉, C₁₇×C₂²⋊(C₄₃⋊C₉), C₅×C₁₇×C₄₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6579, 2);