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C₁₇×C₁₁²⋊C₉ #32915046

order	18513
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₇ · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₁₇×C₁₁²⋊C₉
unambiguous semidirect product	C₁₁²⋊(C₉×C₁₇)
unambiguous semidirect product	(C₁₁²×C₁₇)⋊C₉

Splittings

derived, Sylow	C₁₁² ⋊ C₉×C₁₇
Hall	C₁₁²×C₁₇ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₁₁²⋊C₃
commutator, hypocenter	C₁₁²	C₉×C₁₇
Frattini	C₃	C₁₇×C₁₁²⋊C₃
Fitting, socle, prime radical	C₃×C₁₁²×C₁₇	C₃
cosocle	C₃×C₁₁²	C₃×C₁₇
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₃×C₁₇

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1683

Conjugacy classes & character table

2193 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	C₁₇⋊#14546095
maximal subgroup of	C₁₇×#14546095, C₁₇⋊#14546095, C₁₇×(C₁₁⋊D₁₁)⋊C₉, …
maximal normal subgroup of	C₁₇×#14546095, C₁₇⋊#14546095, C₁₇×(C₁₁⋊D₁₁)⋊C₉, …
maximal quotient of	C₂×C₁₇×C₁₁²⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18513, 4);