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C₂₃×C₂²⋊#4294 #30628565

order	15732
automorphism	?
homology	Abelianization (H₁) = C₉×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₃×C₂²⋊#4294
unambiguous semidirect product	C₂²⋊(C₂₃×#4294)
unambiguous semidirect product	(C₂²×C₂₃)⋊#4294

Splittings

derived, Hall	C₂²×C₁₉ ⋊ C₉×C₂₃
Hall	C₂²×C₁₉×C₂₃ ⋊ C₉
Hall	C₁₉×C₂₃ ⋊ C₂²⋊C₉
Hall	C₂²×C₂₃ ⋊ #4294
Sylow	C₁₉ ⋊ C₂₃×C₂²⋊C₉
Sylow	C₂² ⋊ C₂₃×#4294

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7866

Conjugacy classes & character table

1932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 27);