Finite Group Databasebeta

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C₉×C₁₉×ΓL(1,𝔽₃₂) #40997104

order	26505
automorphism	?
homology	Abelianization (H₁) = C₅×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₉×ΓL(1,𝔽₃₂)
unambiguous semidirect product	(C₉×C₃₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₉×C₁₉×C₃₁)⋊C₅

Splittings

Fitting, Hall	C₉×C₁₉×C₃₁ ⋊ C₅
derived, Sylow	C₃₁ ⋊ C₅×C₉×C₁₉
Hall	C₁₉×C₃₁ ⋊ C₅×C₉
Hall	C₉×C₃₁ ⋊ C₅×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	ΓL(1,𝔽₃₂)
commutator, hypocenter	C₃₁	C₅×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×ΓL(1,𝔽₃₂)
Fitting	C₉×C₁₉×C₃₁	C₅
socle	C₃×C₁₉×C₃₁	C₃×C₅
prime radical	C₃×C₁₉×ΓL(1,𝔽₃₂)	C₃
cosocle	C₃×C₃₁	C₃×C₅×C₁₉
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₉×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5301

Conjugacy classes & character table

1881 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26505, 2);