Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#23723 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | C2×#399 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
972 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)(14,15,18,22,19,23,25,33)(16,24,27,35,28,39,32,20)(17,29,31,43,30,21,36,38)(26,40,42,37,41,45,44,34);(14,16,25,27,19,28,18,32)(15,20,33,24,23,35,22,39)(17,26,36,42,30,41,31,44)(21,37,43,45,29,34,38,40);(14,17)(15,21)(16,26)(18,31)(19,30)(20,34)(22,38)(23,29)(24,40)(25,36)(27,42)(28,41)(32,44)(33,43)(35,37)(39,45);(17,30)(21,29)(26,41)(31,36)(34,37)(38,43)(40,45)(42,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16711);