Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13184 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#106 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19)(20,28,30,44)(21,32)(22,25)(23,37)(24,29,39,45)(26,35)(27,36)(31,46,38,42)(33,40,48,43)(34,47)(41,49);(18,20,23,38,22,30,36,31)(19,24,27,43,25,39,37,40)(21,33,35,29,34,48,49,45)(26,42,32,28,41,46,47,44);(14,15,16,17)(19,25)(24,39)(26,41)(27,37)(28,44)(32,47)(40,43)(42,46)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6172);