Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9781 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#9788 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #390 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
366 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20,19,23,18,22)(16,24,25,29,27,28,26,21)(30,31,33,37,34,36,38,44)(32,35,40,42,39,43,41,45);(15,20,23,22)(21,24,29,28)(30,32,38,40,34,39,33,41)(31,35,37,45,36,43,44,42);(14,16,18,26,19,27,17,25)(15,21,20,24,23,29,22,28)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2776);