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C₁₉×ΓL(1,𝔽₃₂)⋊C₉ #40997109

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

Aliases

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

Splittings

derived, Sylow	C₃₁ ⋊ C₅×C₉×C₁₉
Hall	C₁₉×C₃₁⋊C₉ ⋊ C₅
Hall	C₁₉×ΓL(1,𝔽₃₂) ⋊ C₉
Hall	C₁₉×C₃₁ ⋊ C₅×C₉
Hall	C₃₁⋊C₉ ⋊ C₅×C₁₉
Hall	ΓL(1,𝔽₃₂) ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	(C₃₁⋊C₃)⋊C₅
commutator, hypocenter	C₃₁	C₅×C₉×C₁₉
Frattini	C₃	C₁₉×(C₃₁⋊C₃)⋊C₅
Fitting, 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 ◁ C₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5301

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26505, 7);