Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13263 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | C23 |
| commutator | C22 | C22×C13×C16 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle, prime radical | C23×C13 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19)(20,24)(21,22)(23,25)(26,27,29,33,30,34,37,40,31,28,32,35,38,36,39,41);(14,15,16,17)(19,22)(23,24)(26,28,29,35,30,36,37,41,31,27,32,33,38,34,39,40);(18,20,21,25)(19,23,22,24)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6251);