Finite Group Databasebeta

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C₇×C₉×D₁₃₇ #31772113

order	17262
isoclinism	isoclinic class of D₁₃₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₉×D₁₃₇
unambiguous semidirect product	C₁₃₇⋊(C₂×C₇×C₉)

Splittings

Fitting, Hall	C₇×C₉×C₁₃₇ ⋊ C₂
derived, Sylow	C₁₃₇ ⋊ C₂×C₇×C₉
Hall	C₉×C₁₃₇ ⋊ C₂×C₇
Hall	C₇×C₁₃₇ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	D₁₃₇
commutator, hypocenter	C₁₃₇	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×D₁₃₇
Fitting	C₇×C₉×C₁₃₇	C₂
socle	C₃×C₇×C₁₃₇	C₂×C₃
prime radical	C₃×C₇×D₁₃₇	C₃
cosocle	C₃×C₁₃₇	C₂×C₃×C₇
LCS	G ▷ C₁₃₇
UCS	C₁ ◁ C₇×C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8631

Conjugacy classes & character table

4410 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₉×#10587739, C₉×C₇⋊#10587739, C₉×D₇×D₁₃₇, …
maximal normal subgroup of	C₇×C₉×#10587739, C₉×C₇⋊#10587739, C₉×D₇×D₁₃₇, …
maximal quotient of	C₇×C₉×Dic₁₃₇, C₂×C₇×C₉×D₁₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17262, 3);