C₁₉×#10620323 #27159657

order	12483
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#10620323

Splittings

Fitting, socle, Hall	C₁₉×C₇₃ ⋊ C₉
derived, Sylow	C₇₃ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	#10620323
commutator, hypocenter	C₇₃	C₉×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₇₃	C₉
prime radical	C₁₉×C₇₃⋊C₃	C₃
cosocle	C₇₃⋊C₃	C₃×C₁₉
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₁₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 92
transitive degree	μ_t(G) = 1387

A minimal faithful permutation representation — 2 generators on 92 points:

(2,3,5,4,6,10,8,12,20)(7,14,26,15,27,46,29,35,38)(9,17,33,18,34,57,16,31,41)(11,19,36,22,28,49,40,23,42)(13,24,43,25,44,21,32,55,39)(30,51,66,52,45,63,56,64,48)(37,59,72,60,73,71,50,58,62)(47,53,68,65,69,67,61,54,70)(74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92);(1,2,3,7,5,11,14,28,4,9,19,37,26,47,49,60,6,13,17,35,36,58,59,46,15,30,53,66,40,61,73,65,10,21,24,45,33,20,38,42,22,41,62,70,72,39,29,50,27,48,51,67,68,44,52,12,23,31,54,55,71,64,69,25,8,16,32,56,43,57,63,34,18)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#10620323⋊C₂, #10620323⋊D₁₉, D₁₉×#10620323, …
maximal normal subgroup of	C₁₉×#10620323⋊C₂, #10620323⋊D₁₉, D₁₉×#10620323, …
maximal quotient of	C₂×C₁₉×#10620323

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12483, 7);

C19×#10620323 #27159657