Finite Group Databasebeta

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C₇×C₉×D₁₁₉ #28418366

order	14994
isoclinism	isoclinic class of D₁₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₉×D₁₁₉
unambiguous semidirect product	C₁₇⋊(C₇×C₉×D₇)

Splittings

Fitting, Hall	C₇²×C₉×C₁₇ ⋊ C₂
derived	C₇×C₁₇ ⋊ C₂×C₇×C₉
Hall	C₇²×C₁₇ ⋊ C₂×C₉
Hall	C₇²×C₉ ⋊ D₁₇
Hall	C₉×C₁₇ ⋊ C₇×D₇
Sylow	C₇² ⋊ C₉×D₁₇
Sylow	C₁₇ ⋊ C₇×C₉×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	D₁₁₉
commutator, hypocenter	C₇×C₁₇	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×D₁₁₉
Fitting	C₇²×C₉×C₁₇	C₂
socle	C₃×C₇²×C₁₇	C₂×C₃
prime radical	C₃×C₇×D₁₁₉	C₃
cosocle	C₃×C₇×C₁₇	C₂×C₃×C₇
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₇×C₉

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2142

Conjugacy classes & character table

3843 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₉×D₇×D₁₇, C₉×D₇×D₁₁₉, C₉×(C₇⋊D₇)⋊D₁₇, …
maximal normal subgroup of	C₇×C₉×D₇×D₁₇, C₉×D₇×D₁₁₉, C₉×(C₇⋊D₇)⋊D₁₇, …
maximal quotient of	C₇×C₉×Dic₁₁₉, C₂×C₇×C₉×D₁₁₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14994, 58);