Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#21000 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C2×#121 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | C2×#386 |
| prime radical | C2×C13×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1704 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)(16,20,25,34)(17,27,28,39)(18,23)(19,22)(21,29,36,31)(24,40)(26,35,30,38)(32,37)(33,43)(41,44)(42,45);(14,16)(15,20,22,34)(17,24)(18,30)(19,25)(21,33,36,45)(23,38,37,35)(26,32)(27,44,39,40)(28,41)(29,43)(31,42);(14,17)(15,21)(16,24)(18,31)(19,28)(20,33)(22,36)(23,39)(25,41)(26,43)(27,37)(29,32)(30,42)(34,45)(35,44)(38,40);(16,25)(20,34)(24,41)(26,30)(33,45)(35,38)(40,44)(42,43)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13988);