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C₉×D₈₁₇ #28413652

order	14706
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₈₁₇

Splittings

Fitting, Hall	C₉×C₁₉×C₄₃ ⋊ C₂
derived, Hall	C₁₉×C₄₃ ⋊ C₂×C₉
Hall	C₉×C₄₃ ⋊ D₁₉
Hall	C₉×C₁₉ ⋊ D₄₃
Sylow	C₄₃ ⋊ C₉×D₁₉
Sylow	C₁₉ ⋊ C₉×D₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₈₁₇
commutator, hypocenter	C₁₉×C₄₃	C₂×C₉
Frattini	C₃	C₃×D₈₁₇
Fitting	C₉×C₁₉×C₄₃	C₂
socle, cosocle	C₃×C₁₉×C₄₃	C₂×C₃
prime radical	C₃×D₈₁₇	C₃
LCS	G ▷ C₁₉×C₄₃
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7353

Conjugacy classes & character table

3690 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₉×D₄₃, D₉×D₈₁₇, D₁₇₁⋊D₄₃, …
maximal normal subgroup of	C₉×D₁₉×D₄₃, D₉×D₈₁₇, D₁₇₁⋊D₄₃, …
maximal quotient of	C₉×Dic₈₁₇, C₂×C₉×D₈₁₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14706, 8);