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C₃₁×C₂²⋊(C₁₃⋊C₉) #28408181

order	14508
isoclinism	isoclinic class of C₂²⋊(C₁₃⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₉×C₃₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃₁×C₂²⋊(C₁₃⋊C₉)
unambiguous semidirect product	C₂²⋊(C₃₁×C₁₃⋊C₉)
unambiguous semidirect product	C₁₃⋊(C₃₁×C₂²⋊C₉)

Splittings

derived, Hall	C₂²×C₁₃ ⋊ C₉×C₃₁
Hall	C₂²×C₁₃×C₃₁ ⋊ C₉
Hall	C₁₃×C₃₁ ⋊ C₂²⋊C₉
Hall	C₂²×C₃₁ ⋊ C₁₃⋊C₉
Sylow	C₁₃ ⋊ C₃₁×C₂²⋊C₉
Sylow	C₂² ⋊ C₃₁×C₁₃⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₃₁	C₂²⋊(C₁₃⋊C₃)
commutator, hypocenter	C₂²×C₁₃	C₉×C₃₁
Frattini	C₃	C₃₁×C₂²⋊(C₁₃⋊C₃)
Fitting, socle, prime radical	C₂²×C₃×C₁₃×C₃₁	C₃
cosocle	C₂²×C₃×C₁₃	C₃×C₃₁
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₃×C₃₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7254

Conjugacy classes & character table

1860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14508, 67);