Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13098 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1898 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C13×#3010 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×2−1+4 ◁ G | |
640 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)(16,18,26,33)(17,27,30,39)(19,22)(20,23)(21,29,38,35)(24,41)(25,32,34,43)(28,42)(31,44)(36,40)(37,45);(14,16,18,23,20,26,33,15)(17,24,31,38,30,37,28,21)(19,34,32,22,36,25,43,40)(27,35,42,45,39,29,44,41);(14,17)(15,21)(16,24)(18,31)(19,35)(20,30)(22,39)(23,38)(25,44)(26,37)(27,40)(28,33)(29,36)(32,45)(34,42)(41,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6086);