Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10824 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #381 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#117 ◁ G | |
722 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19)(20,27,29,23)(21,24)(22,25)(26,30)(28,32,33,31);(14,15,16,17)(18,20)(19,23)(21,28)(22,29)(24,31)(25,27)(26,32)(30,33);(19,24,25,26)(23,31,27,32)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3812);