C₇₃×#4296 #27159658

order	12483
isoclinism	isoclinic class of #4296
automorphism	?
homology	Abelianization (H₁) = C₉×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇₃×#4296

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₇₃	#4296
commutator, hypocenter	C₁₉	C₉×C₇₃
Frattini	C₁	G
Fitting, socle	C₁₉×C₇₃	C₉
prime radical	C₁₉⋊C₃×C₇₃	C₃
cosocle	C₁₉⋊C₃	C₃×C₇₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇₃

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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇₃×AGL(1,𝔽₁₉), #4296⋊D₇₃, D₇₃×#4296, …
maximal normal subgroup of	C₇₃×AGL(1,𝔽₁₉), #4296⋊D₇₃, D₇₃×#4296, …
maximal quotient of	C₂×C₇₃×#4296

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12483, 8);

C73×#4296 #27159658