Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33745 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23,26,31)(24,33,37,48)(25,30,28,40)(27,43,42,50)(29,44,34,38)(32,41,46,35)(36,47,39,53)(45,51,49,52);(15,18)(19,21)(22,23)(24,34)(25,40)(26,31)(27,32)(28,30)(29,37)(33,44)(35,43)(36,45)(38,48)(39,49)(41,50)(42,46)(47,52)(51,53);(22,24,35,51,28,39,42,44,26,37,41,52,25,36,27,38)(23,29,43,47,30,45,46,48,31,34,50,53,40,49,32,33);(14,16,17,20)(15,19,18,21)(22,25,26,28)(23,30,31,40)(24,36,37,39)(27,41,42,35)(29,45,34,49)(32,43,46,50)(33,47,48,53)(38,52,44,51)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26733);