Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#23751 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | C2×#400 |
| prime radical | C24×C13 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
664 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)(14,15,18,22,19,23,25,34)(16,24,27,36,28,39,33,20)(17,29,32,43,31,21,37,38)(26,40,41,42,30,44,45,35);(14,16,25,27,19,28,18,33)(15,20,34,24,23,36,22,39)(17,30,37,45,31,26,32,41)(21,35,43,40,29,42,38,44);(14,17,18,32,19,31,25,37)(15,21,22,38,23,29,34,43)(16,26,27,41,28,30,33,45)(20,35,24,40,36,42,39,44);(17,31)(21,29)(26,30)(32,37)(35,42)(38,43)(40,44)(41,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16739);