Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#11000 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #390 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C2×C13 | #1438 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1292 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,28,30,21)(18,31)(19,23)(20,26)(22,33)(25,39,41,45)(27,38)(29,37,44,42)(32,35)(34,43,36,40);(14,16)(15,20)(17,25)(18,32)(19,27)(21,36)(22,38)(23,35)(24,31)(26,33)(28,34)(29,43)(30,41)(37,39)(40,44)(42,45);(14,17)(15,21)(16,25)(18,29)(19,30)(20,34)(22,37)(23,28)(24,39)(26,40)(27,41)(31,42)(32,43)(33,44)(35,36)(38,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3988);