Finite Group Databasebeta

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C₃×D₃×C₄₈₇ #22576850

order	8766
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄₈₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₃×C₄₈₇
unambiguous semidirect product	C₃⋊(C₂×C₃×C₄₈₇)

Splittings

Fitting, socle, Hall	C₃²×C₄₈₇ ⋊ C₂
derived	C₃ ⋊ C₂×C₃×C₄₈₇
Sylow	C₃² ⋊ C₂×C₄₈₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₈₇	D₃
commutator, hypocenter	C₃	C₂×C₃×C₄₈₇
Frattini	C₁	G
Fitting, socle	C₃²×C₄₈₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₄₈₇

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4383 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₃×D₄₈₇, D₃²×C₄₈₇, D₃×D₁₄₆₁, …
maximal normal subgroup of	C₃×D₃×D₄₈₇, D₃²×C₄₈₇, D₃×D₁₄₆₁, …
maximal quotient of	C₃×Dic₃×C₄₈₇, C₂×C₃×D₃×C₄₈₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8766, 15);