Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33438 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C24 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C22×C13 | C23×C8 |
| prime radical | C13×#532 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ G | |
682 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,23,28,24,29,38,45,22,27,36,43,37,44,40,49)(20,30,32,46,33,34,42,48,31,25,39,41,47,21,26,35);(15,17)(18,20)(19,25)(21,29)(22,31)(23,32)(24,33)(26,40)(27,30)(28,41)(34,44)(35,45)(36,39)(37,47)(38,42)(43,46)(48,49);(18,21,23,35,24,30,38,46,22,34,36,48,37,25,40,41)(19,26,28,20,29,32,45,33,27,42,43,31,44,39,49,47);(20,31)(21,34)(25,30)(26,42)(32,39)(33,47)(35,48)(41,46)1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26426);