Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12019 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#12904 |
| 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 | |
318 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)(20,28,30,40)(21,32)(22,25)(23,36)(24,29,37,42)(26,34)(27,35)(31,45,44,41)(33,46)(38,49,48,43)(39,47);(18,20,21,29,23,31,34,43,22,30,33,42,35,44,47,49)(19,24,26,28,27,38,32,41,25,37,39,40,36,48,46,45);(14,15,16,17)(19,25)(24,37)(26,39)(27,36)(28,40)(32,46)(38,48)(41,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5892);