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C₁₃×C₁₇×#4294 #49180245

order	37791
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

C₁₃×C₁₇×#4294

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 37791

Conjugacy classes & character table

5967 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37791, 2);