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C₁₃×C₅⋊(D₁₃⋊C₉) #29503579

order	15210
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₅⋊(D₁₃⋊C₉)
unambiguous semidirect product	C₅⋊(C₁₃×D₁₃⋊C₉)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(D₅×C₁₃)
unambiguous semidirect product	D₆₅⋊(C₉×C₁₃)

Splittings

derived	C₅×C₁₃ ⋊ C₂×C₉×C₁₃
Hall	C₅×C₁₃×C₁₃⋊C₉ ⋊ C₂
Hall	C₁₃×D₆₅ ⋊ C₉
Hall	C₁₃×C₁₃⋊C₉ ⋊ D₅
Hall	C₅×C₁₃² ⋊ C₂×C₉
Sylow	C₁₃² ⋊ C₉×D₅
Sylow	C₅ ⋊ C₁₃×D₁₃⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₅⋊(D₁₃⋊C₃)
commutator, hypocenter	C₅×C₁₃	C₂×C₉×C₁₃
Frattini	C₃	C₁₃×C₅⋊(D₁₃⋊C₃)
Fitting, socle	C₃×C₅×C₁₃²	C₂×C₃
prime radical	C₃×C₁₃×D₆₅	C₃
cosocle	C₃×C₅×C₁₃	C₂×C₃×C₁₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₁₃

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1170

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₃×#63122⋊C₉, C₁₃×#63121⋊C₉, #44477653, …
maximal normal subgroup of	C₁₃×#63122⋊C₉, C₁₃×#63121⋊C₉, #44477653, …
maximal quotient of	C₁₃×Dic₆₅⋊C₉, C₂×C₁₃×C₅⋊(D₁₃⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 42);