Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#9707 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C2×C13×#127 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C43×C13 ◁ G | |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,22)(20,24)(23,25)(26,27,30,31,29,32,28,33);(18,19,20,22,21,23,24,25)(27,31)(28,30)(32,33);(14,15,16,17)(19,23)(22,25)(27,32)(31,33)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2695);