Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11502 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#12795 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#99 |
| commutator | C24 | C22×C4×C13 |
| Frattini, cosocle | C22×D4 | C23×C13 |
| prime radical | C2×C13×#120 | C22 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G | |
600 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)(15,17)(18,19)(20,23)(21,28,29,24)(22,25)(26,32)(27,30,33,31);(14,15,16,17)(18,20)(19,23)(21,27)(22,26)(24,31)(25,32)(28,30)(29,33);(19,24)(20,26)(23,30)(25,28)(27,33)(31,32)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5783);