Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33435 |
| 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 | |
674 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)(18,19,22,28,23,29,37,45,24,27,38,43,39,44,40,49)(20,25,31,41,32,21,33,34,30,35,46,48,47,36,26,42);(15,17)(18,20)(19,25)(21,29)(22,31)(23,32)(24,30)(26,40)(27,35)(28,41)(33,37)(34,45)(36,44)(38,46)(39,47)(42,49)(43,48);(18,21,22,34,23,35,37,48,24,36,38,42,39,25,40,41)(19,26,28,20,29,31,45,32,27,33,43,30,44,46,49,47);(19,27)(20,30)(26,33)(28,43)(29,44)(31,46)(32,47)(45,49)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26423);