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C₉×D₁₃×D₆₁ #43269686

order	28548
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₁₃×D₆₁

Splittings

Fitting, Hall	C₉×C₁₃×C₆₁ ⋊ C₂²
derived, Hall	C₁₃×C₆₁ ⋊ C₂²×C₉
Hall	C₉×C₆₁ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₆₁
Sylow	C₆₁ ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₉×D₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₃×D₆₁
commutator, hypocenter	C₁₃×C₆₁	C₂²×C₉
Frattini	C₃	C₃×D₁₃×D₆₁
Fitting	C₉×C₁₃×C₆₁	C₂²
socle, cosocle	C₃×C₁₃×C₆₁	C₂²×C₃
prime radical	C₃×D₁₃×D₆₁	C₃
LCS	G ▷ C₁₃×C₆₁
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7137

Conjugacy classes & character table

2304 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28548, 72);