C₉×D₈₃ #13093642

order	1494
isoclinism	isoclinic class of D₈₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₈₃
unambiguous semidirect product	C₈₃⋊(C₂×C₉)

Splittings

Fitting, Hall	C₉×C₈₃ ⋊ C₂
derived, Sylow	C₈₃ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₈₃
commutator, hypocenter	C₈₃	C₂×C₉
Frattini	C₃	C₃×D₈₃
Fitting	C₉×C₈₃	C₂
socle, cosocle	C₃×C₈₃	C₂×C₃
prime radical	C₃×D₈₃	C₃
LCS	G ▷ C₈₃
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 92
transitive degree	μ_t(G) = 747

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₉×D₈₃, C₂×C₉×D₈₃, C₉×C₁₁×D₈₃, …
maximal normal subgroup of	D₉×D₈₃, C₂×C₉×D₈₃, C₉×C₁₁×D₈₃, …
maximal quotient of	C₉×Dic₈₃, C₂×C₉×D₈₃, C₉×C₁₁×D₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1494, 2);

C9×D83 #13093642