Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13033 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13035 |
| 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)(14,15,19,26,44,47,43,24,21,28,42,58,20,27,18,25)(16,29,33,22,45,49,31,59,35,62,69,51,34,56,32,50)(17,36,38,55,46,57,37,54,40,52,41,23,39,53,71,60)(30,48,65,73,70,76,64,72,67,75,68,61,66,74,63,77);(14,16,20,45,21,35,44,34)(15,22,47,50,28,51,27,59)(17,30,46,66,40,67,39,70)(18,33,42,31,43,69,19,32)(23,48,54,76,55,75,60,74)(24,56,58,62,25,49,26,29)(36,61,53,77,52,73,57,72)(37,68,41,64,71,65,38,63);(14,17)(15,23)(16,30)(18,41)(19,37)(20,46)(21,40)(22,48)(24,53)(25,57)(26,36)(27,60)(28,55)(29,61)(31,65)(32,68)(33,64)(34,70)(35,67)(38,43)(39,44)(42,71)(45,66)(47,54)(49,72)(50,76)(51,75)(52,58)(56,77)(59,74)(62,73)(63,69)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6023);