Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13030 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13031 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1879 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
456 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)(14,15,19,25,44,47,42,24,21,27,41,58,20,26,18,40)(16,28,31,22,45,49,30,59,33,62,69,51,32,56,43,50)(17,34,37,55,46,57,35,54,39,52,72,23,38,53,36,60)(29,48,65,61,70,77,64,73,67,76,68,71,66,75,63,74);(14,16,20,45,21,33,44,32)(15,22,47,50,27,51,26,59)(17,29,46,66,39,67,38,70)(18,31,41,30,42,69,19,43)(23,48,54,77,55,76,60,75)(24,56,58,62,40,49,25,28)(34,71,53,74,52,61,57,73)(35,68,72,64,36,65,37,63);(14,17)(15,23)(16,29)(18,37)(19,36)(20,46)(21,39)(22,48)(24,57)(25,52)(26,60)(27,55)(28,61)(30,68)(31,63)(32,70)(33,67)(34,58)(35,41)(38,44)(40,53)(42,72)(43,65)(45,66)(47,54)(49,74)(50,77)(51,76)(56,73)(59,75)(62,71)(64,69)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6019);