C₁₃×D₈₃ #14524176

order	2158
isoclinism	isoclinic class of D₈₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₈₃
unambiguous semidirect product	C₈₃⋊(C₂×C₁₃)

Splittings

Fitting, socle, Hall	C₁₃×C₈₃ ⋊ C₂
derived, Sylow	C₈₃ ⋊ C₂×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₈₃
commutator, cosocle, hypocenter	C₈₃	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₈₃	C₂
LCS	G ▷ C₈₃
UCS	C₁ ◁ C₁₃

8 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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₃×D₈₃, C₂×C₁₃×D₈₃, C₇×C₁₃×D₈₃, …
maximal normal subgroup of	D₁₃×D₈₃, C₂×C₁₃×D₈₃, C₇×C₁₃×D₈₃, …
maximal quotient of	C₁₃×Dic₈₃, C₂×C₁₃×D₈₃, C₇×C₁₃×D₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2158, 2);

C13×D83 #14524176