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C₂×C₄₃₉⋊C₉ #21463618

order	7902
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₄₃₉⋊C₉
unambiguous semidirect product	(C₂×C₄₃₉)⋊C₉

Splittings

derived, Sylow	C₄₃₉ ⋊ C₂×C₉
Hall	C₂×C₄₃₉ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₄₃₉⋊C₃
commutator, hypocenter	C₄₃₉	C₂×C₉
Frattini	C₃	C₂×C₄₃₉⋊C₃
Fitting, socle	C₂×C₃×C₄₃₉	C₃
LCS	G ▷ C₄₃₉
UCS	C₁ ◁ C₂×C₃

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

894 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₄₃₉⋊C₉, C₄×C₄₃₉⋊C₉, C₂×D₄₃₉⋊C₉, …
maximal normal subgroup of	Dic₄₃₉⋊C₉, C₄×C₄₃₉⋊C₉, C₂×D₄₃₉⋊C₉, …
maximal quotient of	C₄×C₄₃₉⋊C₉, C₂²×C₄₃₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7902, 3);