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C₁₃⋊C₉×C₁₆₃ #34040169

order	19071
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₆₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃⋊C₉×C₁₆₃
unambiguous semidirect product	C₁₃⋊(C₉×C₁₆₃)

Splittings

derived, Sylow	C₁₃ ⋊ C₉×C₁₆₃
Hall	C₁₃×C₁₆₃ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₆₃	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₉×C₁₆₃
Frattini	C₃	C₁₃⋊C₃×C₁₆₃
Fitting, socle, prime radical	C₃×C₁₃×C₁₆₃	C₃
cosocle	C₃×C₁₃	C₃×C₁₆₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₆₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 19071

Conjugacy classes & character table

3423 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₃⋊C₉×C₁₆₃, C₁₃⋊C₉×D₁₆₃, C₁₆₃×D₁₃⋊C₉, …
maximal normal subgroup of	C₂×C₁₃⋊C₉×C₁₆₃, C₁₃⋊C₉×D₁₆₃, C₁₆₃×D₁₃⋊C₉, …
maximal quotient of	C₂×C₁₃⋊C₉×C₁₆₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19071, 2);