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C₇×D₉×C₆₇ #22554722

order	8442
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₉×C₆₇
unambiguous semidirect product	C₉⋊(C₂×C₇×C₆₇)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₆₇	D₉
commutator, hypocenter	C₉	C₂×C₇×C₆₇
Frattini	C₃	D₃×C₇×C₆₇
Fitting	C₇×C₉×C₆₇	C₂
socle	C₃×C₇×C₆₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₇×C₆₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2814 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₉×D₆₇, D₇×D₉×C₆₇, D₉×D₄₆₉, …
maximal normal subgroup of	C₇×D₉×D₆₇, D₇×D₉×C₆₇, D₉×D₄₆₉, …
maximal quotient of	C₇×Dic₉×C₆₇, C₂×C₇×D₉×C₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8442, 9);