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C₁₇×C₁₉×C₁₃⋊C₉ #49180246

order	37791
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₁₉×C₁₃⋊C₉
unambiguous semidirect product	C₁₃⋊(C₉×C₁₇×C₁₉)
unambiguous semidirect product	(C₁₃×C₁₇)⋊(C₉×C₁₉)

Splittings

derived, Sylow	C₁₃ ⋊ C₉×C₁₇×C₁₉
Hall	C₁₃×C₁₇×C₁₉ ⋊ C₉
Hall	C₁₃×C₁₉ ⋊ C₉×C₁₇
Hall	C₁₃×C₁₇ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇×C₁₉	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₉×C₁₇×C₁₉
Frattini	C₃	C₁₇×C₁₉×C₁₃⋊C₃
Fitting, socle, prime radical	C₃×C₁₃×C₁₇×C₁₉	C₃
cosocle	C₃×C₁₃	C₃×C₁₇×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₇×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 37791

Conjugacy classes & character table

6783 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37791, 3);