Finite Group Databasebeta

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C₁₃×C₂²⋊C₉×C₅₃ #37613624

order	24804
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃×C₅₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×C₂²⋊C₉×C₅₃
unambiguous semidirect product	C₂²⋊(C₉×C₁₃×C₅₃)

Splittings

derived, Sylow	C₂² ⋊ C₉×C₁₃×C₅₃
Hall	C₂²×C₁₃×C₅₃ ⋊ C₉
Hall	C₂²×C₅₃ ⋊ C₉×C₁₃
Hall	C₂²×C₁₃ ⋊ C₉×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₅₃	A₄
commutator, hypocenter	C₂²	C₉×C₁₃×C₅₃
Frattini	C₃	A₄×C₁₃×C₅₃
Fitting, socle, prime radical	C₂²×C₃×C₁₃×C₅₃	C₃
cosocle	C₂²×C₃	C₃×C₁₃×C₅₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₁₃×C₅₃

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12402

Conjugacy classes & character table

8268 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 56);