Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13322 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,25,31)(20,32,37,63)(21,38,41,60)(22,42,47,58)(23,30,24,29)(26,49,53,34)(27,48,55,40)(28,45,59,46)(33,64,67,81)(35,56,36,62)(39,57,44,54)(43,51,69,52)(50,73,80,76)(61,70,78,66)(65,71,68,79)(72,77,75,74);(14,15)(16,17)(18,20,25,37)(19,26,31,53)(21,33,41,67)(22,43,47,69)(23,36,24,35)(27,50,55,80)(28,56,59,62)(29,52,30,51)(32,58,63,42)(34,45,49,46)(38,71,60,79)(39,73,44,76)(40,70,48,66)(54,81,57,64)(61,72,78,75)(65,77,68,74);(15,17)(18,21)(19,27)(20,33)(22,44)(23,48)(24,40)(25,41)(26,50)(28,57)(29,60)(30,38)(31,55)(32,61)(34,68)(35,70)(36,66)(37,67)(39,47)(42,75)(43,76)(45,74)(46,77)(49,65)(51,71)(52,79)(53,80)(54,59)(56,64)(58,72)(62,81)(63,78)(69,73)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6310);