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C₅×C₁₉×C₃₁⋊C₉ #40997105

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

Aliases

direct product	C₅×C₁₉×C₃₁⋊C₉
unambiguous semidirect product	(C₅×C₃₁)⋊(C₉×C₁₉)

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 26505

Conjugacy classes & character table

3705 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26505, 3);