Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#21785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2308 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26,30,21)(17,23,18,32)(19,25)(20,24)(22,31,40,33)(27,43)(28,37)(29,42,34,38)(35,41)(36,44)(39,45);(14,16)(15,21)(17,27)(18,28)(19,34)(20,30)(22,39)(23,37)(24,26)(25,42)(29,35)(31,45)(32,43)(33,44)(36,40)(38,41);(14,17,20,18)(15,22,24,40)(16,27,30,28)(19,33,35,31)(21,36,26,39)(23,25,32,41)(29,45,34,44)(37,38,43,42);(14,18,20,17)(15,23,24,32)(16,28,30,27)(19,33,35,31)(21,37,26,43)(22,25,40,41)(29,45,34,44)(36,38,39,42)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14773);