Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2180 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#12677 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #442 |
| commutator | C8 | C2×C42×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | AGL(1,ℤ/8) |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#97 ◁ G | |
318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,21,27,22,28,31,26,23,29,33,24,32,25,20,30);(14,15,16,17)(19,24)(20,21)(22,32)(25,30)(26,28)(27,29)(31,33);(19,25,29,28)(20,31)(21,33)(24,30,27,26)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5665);