C₉×D₇₃ #13050267

order	1314
isoclinism	isoclinic class of D₇₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₉×D₇₃

Splittings

Fitting, Hall	C₉×C₇₃ ⋊ C₂
derived, Sylow	C₇₃ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇₃
commutator, hypocenter	C₇₃	C₂×C₉
Frattini	C₃	C₃×D₇₃
Fitting	C₉×C₇₃	C₂
socle, cosocle	C₃×C₇₃	C₂×C₃
prime radical	C₃×D₇₃	C₃
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 82
transitive degree	μ_t(G) = 657

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×#64408, C₉⋊#64408, D₉×D₇₃, …
maximal normal subgroup of	C₉×#64408, C₉⋊#64408, D₉×D₇₃, …
maximal quotient of	C₉×Dic₇₃, C₂×C₉×D₇₃, C₉×C₁₁×D₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1314, 4);

C9×D73 #13050267