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C₁₃₉×D₁₃⋊C₉ #45654229

order	32526
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃₉×D₁₃⋊C₉
unambiguous semidirect product	D₁₃⋊(C₉×C₁₃₉)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₂×C₁₃₉)

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₁₃₉
Hall	C₁₃⋊C₉×C₁₃₉ ⋊ C₂
Hall	D₁₃×C₁₃₉ ⋊ C₉
Hall	C₁₃×C₁₃₉ ⋊ C₂×C₉
Hall	C₁₃⋊C₉ ⋊ C₂×C₁₃₉
Hall	D₁₃ ⋊ C₉×C₁₃₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃₉	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₉×C₁₃₉
Frattini	C₃	D₁₃⋊C₃×C₁₃₉
Fitting, socle	C₃×C₁₃×C₁₃₉	C₂×C₃
prime radical	C₃×D₁₃×C₁₃₉	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₁₃₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₃₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16263

Conjugacy classes & character table

3336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32526, 18);