Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13008 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #481 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1874 |
| prime radical | C13×#3054 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C22×C13×M16 ◁ G | |
516 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)(14,15,18,23,19,24,35,41,20,22,17,30,32,39,33,43)(16,25,28,38,29,40,34,37,27,44,26,42,36,45,31,21);(14,16)(15,21,22,37)(17,31)(18,34)(19,36)(20,27)(23,40,30,45)(24,42,39,38)(25,43,44,41)(26,33)(28,35)(29,32);(15,22)(17,18)(21,37)(24,39)(26,28)(31,34)(33,35)(38,42)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5996);