Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23474 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #393 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| socle | C2×C13 | C2×#393 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1164 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)(16,20)(17,27,30,21)(18,22)(19,23)(24,37,28,32)(25,33)(26,34)(29,40,42,35)(31,36)(38,45,41,43)(39,44);(14,16)(15,20)(17,28,30,24)(18,25)(19,26)(21,32,27,37)(22,33)(23,34)(29,41,42,38)(31,39)(35,43,40,45)(36,44);(14,17)(15,21)(16,24)(18,29)(19,30)(20,32)(22,35)(23,27)(25,38)(26,28)(31,42)(33,43)(34,37)(36,40)(39,41)(44,45);(14,18,19,31)(15,22,23,36)(16,25,26,39)(17,29,30,42)(20,33,34,44)(21,35,27,40)(24,38,28,41)(32,43,37,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16462);