Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33401 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | C22×D4 |
| commutator | C4 | C23×C8×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C22×C4⋊C8 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C2×C13×#131 ◁ G | |
684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,25,20,24,30,40,21,26,29,22,18,35,16,27)(17,23,33,39,34,38,42,45,31,37,43,36,32,44,28,41);(14,16,18,29,21,30,20,19)(15,22,24,27,26,25,35,40)(17,28,32,43,31,42,34,33)(23,36,38,41,37,39,44,45);(14,17)(15,23)(16,28)(18,32)(19,33)(20,34)(21,31)(22,36)(24,38)(25,39)(26,37)(27,41)(29,43)(30,42)(35,44)(40,45);(17,31)(23,37)(28,42)(32,34)(33,43)(36,39)(38,44)(41,45)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26389);