Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13005 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1874 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
492 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)(14,15,20,26,19,25,36,24,22,27,35,38,21,16,18,29)(17,28,32,43,37,23,34,41,33,44,39,40,31,42,30,45);(14,16,19,27,22,25,21,15)(17,28,37,42,33,44,31,23)(18,29,20,38,36,24,35,26)(30,43,32,45,34,40,39,41);(14,17)(15,23)(16,28)(18,34)(19,37)(20,39)(21,31)(22,33)(24,43)(25,44)(26,45)(27,42)(29,40)(30,36)(32,35)(38,41)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5995);