#261×C₈₃ #16864451

order	4316
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₄×C₈₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

#261×C₈₃

Splittings

Fitting, socle, Hall	C₁₃×C₈₃ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₄×C₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₈₃	#261
commutator, hypocenter	C₁₃	C₄×C₈₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₈₃	C₄
prime radical	D₁₃×C₈₃	C₂
cosocle	D₁₃	C₂×C₈₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₈₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 96
transitive degree	μ_t(G) = 1079

A minimal faithful permutation representation — 2 generators on 96 points:

(2,3,4,6)(5,8,9,13)(7,11,12,10)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96);(1,2,5,8,12,6,10,11,3,7,13,9,4)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₈₃×AGL(1,𝔽₁₃), C₃×#261×C₈₃, C₈₃×C₃⋊#261, …
maximal normal subgroup of	C₈₃×AGL(1,𝔽₁₃), C₃×#261×C₈₃, C₅×#261×C₈₃, …
maximal quotient of	C₃×#261×C₈₃, C₈₃×C₃⋊#261, C₅×#261×C₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4316, 6);

#261×C83 #16864451