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C₁₇×C₆₁⋊C₉ #22605386

order	9333
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₆₁⋊C₉
unambiguous semidirect product	C₆₁⋊(C₉×C₁₇)
unambiguous semidirect product	(C₁₇×C₆₁)⋊C₉

Splittings

derived, Sylow	C₆₁ ⋊ C₉×C₁₇
Hall	C₁₇×C₆₁ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₆₁⋊C₃
commutator, hypocenter	C₆₁	C₉×C₁₇
Frattini	C₃	C₁₇×C₆₁⋊C₃
Fitting, socle	C₃×C₁₇×C₆₁	C₃
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₃×C₁₇

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1173 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₇×C₆₁⋊C₉, C₁₇×D₆₁⋊C₉, D₁₇×C₆₁⋊C₉, …
maximal normal subgroup of	C₂×C₁₇×C₆₁⋊C₉, C₁₇×D₆₁⋊C₉, D₁₇×C₆₁⋊C₉, …
maximal quotient of	C₂×C₁₇×C₆₁⋊C₉, C₁₇×C₂²⋊(C₆₁⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9333, 2);