Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12792 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #121 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1797 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
440 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)(14,15,19,26,20,24,31,39,21,27,30,22,18,25,16,28)(17,32,35,44,34,41,29,43,36,42,37,45,33,23,40,38);(14,16,18,30,21,31,20,19)(15,22,24,28,27,26,25,39)(17,29,33,35,36,40,34,37)(23,38,32,44,41,43,42,45);(14,17)(15,23)(16,29)(18,33)(19,37)(20,34)(21,36)(22,38)(24,32)(25,42)(26,43)(27,41)(28,44)(30,35)(31,40)(39,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5780);