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C₆₇×D₆₃ #22554724

order	8442
isoclinism	isoclinic class of D₆₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₇×D₆₃
unambiguous semidirect product	C₇⋊(D₉×C₆₇)
unambiguous semidirect product	C₉⋊(D₇×C₆₇)

Splittings

Fitting, Hall	C₇×C₉×C₆₇ ⋊ C₂
derived, Hall	C₇×C₉ ⋊ C₂×C₆₇
Hall	C₉×C₆₇ ⋊ D₇
Hall	C₇×C₆₇ ⋊ D₉
Sylow	C₉ ⋊ D₇×C₆₇
Sylow	C₇ ⋊ D₉×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₆₇	D₆₃
commutator, hypocenter	C₇×C₉	C₂×C₆₇
Frattini	C₃	D₂₁×C₆₇
Fitting	C₇×C₉×C₆₇	C₂
socle	C₃×C₇×C₆₇	D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₆₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2211 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₆₃×D₆₇, D₇×D₉×C₆₇, D₆₃⋊D₆₇, …
maximal normal subgroup of	D₆₃×D₆₇, D₇×D₉×C₆₇, D₆₃⋊D₆₇, …
maximal quotient of	C₆₇×Dic₆₃, C₂×C₆₇×D₆₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8442, 11);