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C₉×D₈₃₃ #28418316

order	14994
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₈₃₃
unambiguous semidirect product	C₁₇⋊(C₉×D₄₉)

Splittings

Fitting, Hall	C₉×C₁₇×C₄₉ ⋊ C₂
derived, Hall	C₁₇×C₄₉ ⋊ C₂×C₉
Hall	C₉×C₄₉ ⋊ D₁₇
Hall	C₉×C₁₇ ⋊ D₄₉
Sylow	C₄₉ ⋊ C₉×D₁₇
Sylow	C₁₇ ⋊ C₉×D₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₈₃₃
commutator, hypocenter	C₁₇×C₄₉	C₂×C₉
Frattini	C₃×C₇	C₃×D₁₁₉
Fitting	C₉×C₁₇×C₄₉	C₂
socle	C₃×C₇×C₁₇	C₃×D₇
prime radical	C₃×D₈₃₃	C₃
cosocle	C₃×C₁₇×C₄₉	C₂×C₃
LCS	G ▷ C₁₇×C₄₉
UCS	C₁ ◁ C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7497

Conjugacy classes & character table

3762 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₇×D₄₉, D₉×D₈₃₃, D₁₅₃⋊D₄₉, …
maximal normal subgroup of	C₉×D₁₇×D₄₉, D₉×D₈₃₃, D₁₅₃⋊D₄₉, …
maximal quotient of	C₉×Dic₈₃₃, C₂×C₉×D₈₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14994, 8);