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C₅×C₉×C₁₃⋊D₁₃ #29503594

order	15210
isoclinism	isoclinic class of C₁₃⋊D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁₃

Aliases

C₅×C₉×C₁₃⋊D₁₃

Splittings

Fitting, Hall	C₅×C₉×C₁₃² ⋊ C₂
derived, Sylow	C₁₃² ⋊ C₂×C₅×C₉
Hall	C₉×C₁₃² ⋊ C₂×C₅
Hall	C₅×C₁₃² ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	C₁₃⋊D₁₃
commutator, hypocenter	C₁₃²	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×C₁₃⋊D₁₃
Fitting	C₅×C₉×C₁₃²	C₂
socle	C₃×C₅×C₁₃²	C₂×C₃
prime radical	C₃×C₅×C₁₃⋊D₁₃	C₃
cosocle	C₃×C₁₃²	C₂×C₃×C₅
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₅×C₉

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7605

Conjugacy classes & character table

3870 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×#10621728, C₅×C₉×#10621729, C₅×C₉×D₁₃², …
maximal normal subgroup of	C₅×C₉×#10621728, C₅×C₉×#10621729, C₅×C₉×D₁₃², …
maximal quotient of	C₅×C₉×#10621725, C₂×C₅×C₉×C₁₃⋊D₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 57);