Finite Group Databasebeta

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C₁₃×C₂²⋊(C₆₁⋊C₉) #43269702

order	28548
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×C₂²⋊(C₆₁⋊C₉)
unambiguous semidirect product	C₂²⋊(C₁₃×C₆₁⋊C₉)
unambiguous semidirect product	C₆₁⋊(C₁₃×C₂²⋊C₉)

Splittings

derived, Hall	C₂²×C₆₁ ⋊ C₉×C₁₃
Hall	C₂²×C₁₃×C₆₁ ⋊ C₉
Hall	C₁₃×C₆₁ ⋊ C₂²⋊C₉
Sylow	C₆₁ ⋊ C₁₃×C₂²⋊C₉
Hall	C₂²×C₁₃ ⋊ C₆₁⋊C₉
Sylow	C₂² ⋊ C₁₃×C₆₁⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₂²⋊(C₆₁⋊C₃)
commutator, hypocenter	C₂²×C₆₁	C₉×C₁₃
Frattini	C₃	C₁₃×C₂²⋊(C₆₁⋊C₃)
Fitting, socle, prime radical	C₂²×C₃×C₁₃×C₆₁	C₃
cosocle	C₂²×C₃×C₆₁	C₃×C₁₃
LCS	G ▷ C₂²×C₆₁
UCS	C₁ ◁ C₃×C₁₃

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 14274

Conjugacy classes & character table

3276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28548, 88);