Finite Group Databasebeta

← Prev (#20268697) Next (#20268699) →

C₂×C₃₆₇⋊C₉ #20268698

order	6606
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₃₆₇⋊C₉
unambiguous semidirect product	(C₂×C₃₆₇)⋊C₉

Splittings

derived, Sylow	C₃₆₇ ⋊ C₂×C₉
Hall	C₂×C₃₆₇ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃₆₇⋊C₃
commutator, hypocenter	C₃₆₇	C₂×C₉
Frattini	C₃	C₂×C₃₆₇⋊C₃
Fitting, socle	C₂×C₃×C₃₆₇	C₃
LCS	G ▷ C₃₆₇
UCS	C₁ ◁ C₂×C₃

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

750 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₃₆₇⋊C₉, C₄×C₃₆₇⋊C₉, C₂×D₃₆₇⋊C₉, …
maximal normal subgroup of	Dic₃₆₇⋊C₉, C₄×C₃₆₇⋊C₉, C₂×D₃₆₇⋊C₉, …
maximal quotient of	C₄×C₃₆₇⋊C₉, C₂²×C₃₆₇⋊C₉, C₂×C₅×C₃₆₇⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6606, 3);