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C₅×(C₁₃⋊C₉)⋊D₁₃ #29503576

order	15210
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×(C₁₃⋊C₉)⋊D₁₃
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₅×D₁₃)

Splittings

derived, Sylow	C₁₃² ⋊ C₂×C₅×C₉
Hall	C₅×C₁₃×C₁₃⋊C₉ ⋊ C₂
Hall	C₅×C₁₃⋊D₁₃ ⋊ C₉
Hall	C₁₃×C₁₃⋊C₉ ⋊ C₂×C₅
Hall	C₅×C₁₃² ⋊ C₂×C₉
Hall	C₁₃⋊D₁₃ ⋊ C₅×C₉

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 585

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×#20258774, C₅×#20258775, C₅×D₁₃×D₁₃⋊C₉, …
maximal normal subgroup of	C₅×#20258774, C₅×#20258775, C₅×D₁₃×D₁₃⋊C₉, …
maximal quotient of	C₅×#20258756, C₂×C₅×(C₁₃⋊C₉)⋊D₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 39);