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C₂×C₉×C₂₃×D₁₉ #30628567

order	15732
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×C₂₃×D₁₉

Splittings

Fitting	C₂×C₉×C₁₉×C₂₃ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂²×C₉×C₂₃
Hall	C₉×C₁₉×C₂₃ ⋊ C₂²
Hall	C₁₉×C₂₃ ⋊ C₂²×C₉
Hall	C₉×C₁₉ ⋊ C₂²×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₂₃	D₁₉
commutator, hypocenter	C₁₉	C₂²×C₉×C₂₃
Frattini	C₃	C₂×C₃×C₂₃×D₁₉
Fitting	C₂×C₉×C₁₉×C₂₃	C₂
socle	C₂×C₃×C₁₉×C₂₃	C₂×C₃
prime radical	C₂×C₃×C₂₃×D₁₉	C₃
cosocle	C₃×C₁₉	C₂²×C₃×C₂₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₉×C₂₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7866

Conjugacy classes & character table

4554 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 29);