Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12980 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C2×D4 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C8×D4 |
| prime radical | C2×C13×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ C22×C13×C16 ◁ G | |
470 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)(18,19,23,29,24,30,43,34,25,31,44,48,22,28,33,46)(20,32,27,47,35,21,37,39,36,38,41,49,40,26,45,42);(14,15,16,17)(18,20,33,37,22,40,44,27,25,36,43,45,24,35,23,41)(19,26,46,47,28,38,48,42,31,21,34,49,30,32,29,39);(18,21)(19,27)(20,34)(22,32)(23,42)(24,38)(25,26)(28,45)(29,40)(30,37)(31,41)(33,49)(35,48)(36,46)(39,44)(43,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5968);