Finite Group Databasebeta

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C₂²×C₂₃×#4294 #30628563

order	15732
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₂₃×#4294

Splittings

derived, Sylow	C₁₉ ⋊ C₂²×C₉×C₂₃
Hall	C₂²×C₁₉×C₂₃ ⋊ C₉
Hall	C₁₉×C₂₃ ⋊ C₂²×C₉
Hall	C₂²×C₁₉ ⋊ C₉×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₂₃	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₉×C₂₃
Frattini	C₃	C₂²×C₂₃×C₁₉⋊C₃
Fitting, socle, prime radical	C₂²×C₃×C₁₉×C₂₃	C₃
cosocle	C₃×C₁₉	C₂²×C₃×C₂₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₃×C₂₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15732

Conjugacy classes & character table

2484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 25);