Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13156 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1936 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
306 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)(15,21,25,32)(16,27,30,35)(17,22)(18,33)(19,36)(23,38)(24,41,34,26)(29,43,39,31)(37,42)(40,44);(14,15,22,24,36,41,17,32,20,25,18,34,19,26,33,21)(16,28,35,44,43,23,39,40,30,45,27,37,31,38,29,42);(14,16,17,29,19,31,22,27,20,30,33,39,36,43,18,35)(15,23,21,37,26,28,34,40,25,38,32,44,41,45,24,42)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6144);