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D₃×D₇×C₈₉ #21418779

order	7476
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₇×C₈₉
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₈₉)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₈₉)
unambiguous semidirect product	D₂₁⋊(C₂×C₈₉)

Splittings

Fitting, socle, Hall	C₃×C₇×C₈₉ ⋊ C₂²
derived, Hall	C₃×C₇ ⋊ C₂²×C₈₉
Hall	C₇×C₈₉ ⋊ C₂×D₃
Hall	C₃×C₈₉ ⋊ C₂×D₇
Sylow	C₇ ⋊ C₂×D₃×C₈₉
Sylow	C₃ ⋊ C₂×D₇×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₈₉	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₈₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₈₉	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₈₉

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1335 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇×D₉×C₈₉, D₃×AGL(1,𝔽₇)×C₈₉, C₃×D₃×D₇×C₈₉, …
maximal normal subgroup of	D₃×AGL(1,𝔽₇)×C₈₉, C₃×D₃×D₇×C₈₉, C₅×D₃×D₇×C₈₉
maximal quotient of	D₇×D₉×C₈₉, C₃×D₃×D₇×C₈₉, D₃×D₂₁×C₈₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7476, 27);