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C₉×D₈₃₉ #28419113

order	15102
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₈₃₉
unambiguous semidirect product	C₈₃₉⋊(C₂×C₉)

Splittings

Fitting, Hall	C₉×C₈₃₉ ⋊ C₂
derived, Sylow	C₈₃₉ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₈₃₉
commutator, hypocenter	C₈₃₉	C₂×C₉
Frattini	C₃	C₃×D₈₃₉
Fitting	C₉×C₈₃₉	C₂
socle, cosocle	C₃×C₈₃₉	C₂×C₃
prime radical	C₃×D₈₃₉	C₃
LCS	G ▷ C₈₃₉
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7551

Conjugacy classes & character table

3789 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×D₈₃₉, C₂×C₉×D₈₃₉
maximal normal subgroup of	D₉×D₈₃₉, C₂×C₉×D₈₃₉
maximal quotient of	C₉×Dic₈₃₉, C₂×C₉×D₈₃₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15102, 3);