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C₉×C₄₃⋊C₄₉ #34038896

order	18963
automorphism	?
homology	Abelianization (H₁) = C₉×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₄₃⋊C₄₉
unambiguous semidirect product	(C₉×C₄₃)⋊C₄₉

Splittings

derived, Sylow	C₄₃ ⋊ C₉×C₄₉
Hall	C₉×C₄₃ ⋊ C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	C₄₃⋊C₇
commutator, hypocenter	C₄₃	C₉×C₄₉
Frattini	C₃×C₇	C₃×C₄₃⋊C₇
Fitting	C₇×C₉×C₄₃	C₇
socle, prime radical, cosocle	C₃×C₇×C₄₃	C₃×C₇
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₇×C₉

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18963

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×D₄₃⋊C₄₉, D₉×C₄₃⋊C₄₉, C₉⋊(D₄₃⋊C₄₉), …
maximal normal subgroup of	C₉×D₄₃⋊C₄₉, D₉×C₄₃⋊C₄₉, C₉⋊(D₄₃⋊C₄₉), …
maximal quotient of	C₂×C₉×C₄₃⋊C₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18963, 3);