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C₂×(C₃₁⋊C₉)⋊D₁₃ #28408162

order	14508
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×(C₃₁⋊C₉)⋊D₁₃
unambiguous semidirect product	(C₂×C₃₁⋊C₉)⋊D₁₃

Splittings

derived, Hall	C₁₃×C₃₁ ⋊ C₂²×C₉
Hall	C₁₃×C₃₁⋊C₉ ⋊ C₂²
Hall	C₂×D₄₀₃ ⋊ C₉
Hall	C₃₁⋊C₉ ⋊ C₂×D₁₃
Sylow	C₃₁ ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×D₃₁⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₃₁⋊C₃)⋊D₁₃
commutator, hypocenter	C₁₃×C₃₁	C₂²×C₉
Frattini	C₃	C₂×(C₃₁⋊C₃)⋊D₁₃
Fitting, socle	C₂×C₃×C₁₃×C₃₁	C₂×C₃
prime radical	C₂×C₃×D₄₀₃	C₃
cosocle	C₃×C₁₃×C₃₁	C₂²×C₃
LCS	G ▷ C₁₃×C₃₁
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7254

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14508, 48);