Finite Group Databasebeta

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C₁₃₇×D₁₃⋊C₉ #44545389

order	32058
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃₇×D₁₃⋊C₉
unambiguous semidirect product	D₁₃⋊(C₉×C₁₃₇)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₂×C₁₃₇)
unambiguous semidirect product	(D₁₃×C₁₃₇)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₁₃₇
Hall	C₁₃⋊C₉×C₁₃₇ ⋊ C₂
Hall	D₁₃×C₁₃₇ ⋊ C₉
Hall	C₁₃×C₁₃₇ ⋊ C₂×C₉
Hall	C₁₃⋊C₉ ⋊ C₂×C₁₃₇
Hall	D₁₃ ⋊ C₉×C₁₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₉×C₁₃₇
Frattini	C₃	D₁₃⋊C₃×C₁₃₇
Fitting, socle	C₃×C₁₃×C₁₃₇	C₂×C₃
prime radical	C₃×D₁₃×C₁₃₇	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₁₃₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₃₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16029

Conjugacy classes & character table

3288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32058, 11);