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C₉×D₈₇₁ #30627886

order	15678
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₈₇₁

Splittings

Fitting, Hall	C₉×C₁₃×C₆₇ ⋊ C₂
derived, Hall	C₁₃×C₆₇ ⋊ C₂×C₉
Hall	C₉×C₆₇ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ D₆₇
Sylow	C₆₇ ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×D₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₈₇₁
commutator, hypocenter	C₁₃×C₆₇	C₂×C₉
Frattini	C₃	C₃×D₈₇₁
Fitting	C₉×C₁₃×C₆₇	C₂
socle, cosocle	C₃×C₁₃×C₆₇	C₂×C₃
prime radical	C₃×D₈₇₁	C₃
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7839

Conjugacy classes & character table

3933 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₃×D₆₇, D₉×D₈₇₁, D₁₁₇⋊D₆₇, …
maximal normal subgroup of	C₉×D₁₃×D₆₇, D₉×D₈₇₁, D₁₁₇⋊D₆₇, …
maximal quotient of	C₉×Dic₈₇₁, C₂×C₉×D₈₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15678, 8);