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C₂×C₇×C₆₇⋊C₉ #22554715

order	8442
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇×C₆₇⋊C₉, C₇×Dic₆₇⋊C₉, Dic₇×C₆₇⋊C₉, …
maximal normal subgroup of	C₄×C₇×C₆₇⋊C₉, C₇×Dic₆₇⋊C₉, Dic₇×C₆₇⋊C₉, …
maximal quotient of	C₄×C₇×C₆₇⋊C₉, C₂²×C₇×C₆₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8442, 2);