Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13525 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #2092 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,24,43,59,19,25,21,27,45,61,20,26,44,60)(16,28,30,50,32,49,31,52,34,62,46,51,33,57,41,22)(17,35,37,23,47,54,42,63,40,58,72,56,39,70,38,55)(29,53,65,64,36,71,69,77,68,76,73,75,67,48,66,74);(14,16,21,34)(15,22,27,52)(17,36)(18,41,45,31)(19,46,44,30)(20,32,43,33)(23,53)(24,57,61,49)(25,62,60,28)(26,50,59,51)(29,47)(35,64)(37,65)(38,69)(39,68)(40,67)(42,66)(48,63)(54,74)(55,71)(56,76)(58,75)(70,77)(72,73);(14,17)(15,23)(16,29)(18,42)(19,37)(20,47)(21,40)(22,48)(24,58)(25,54)(26,63)(27,56)(28,64)(30,69)(31,65)(32,67)(33,36)(34,68)(35,61)(38,45)(39,43)(41,73)(44,72)(46,66)(49,74)(50,76)(51,53)(52,71)(55,59)(57,77)(60,70)(62,75)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6513);