Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13248 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1972 |
| 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 | |
394 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)(16,28)(17,35,39,65)(18,41)(19,24)(20,45)(21,27)(22,31)(23,38,52,59)(25,43)(26,42)(29,54)(30,46,62,75)(32,48)(33,55)(34,58)(36,66,68,50)(37,69,71,53)(40,73,70,51)(44,57)(47,63)(49,64)(56,61,76,67)(60,74,72,77);(14,16,29,32,20,33,18,31,21,34,19,44,42,63,43,64)(15,22,25,55,26,48,24,28,27,49,41,47,45,57,54,58)(17,36,38,72,40,62,71,61,39,68,59,60,70,30,37,67)(23,50,65,76,53,75,73,77,52,66,35,56,69,46,51,74);(14,17,19,38,20,40,43,71,21,39,29,59,42,70,18,37)(15,23,25,35,26,53,24,51,27,52,41,65,45,69,54,73)(16,30,32,61,33,36,31,60,34,62,44,67,63,68,64,72)(22,46,47,74,48,50,58,76,49,75,55,77,57,66,28,56)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6236);