Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#9043 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #120 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G | |
678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,20,24,22,25,21,23)(26,27,30,34,31,35,29,33)(28,36,38,32,39,40,37,41);(14,15,16,17)(19,23)(20,21)(24,25)(26,28)(27,32)(29,38)(30,37)(31,39)(33,40)(34,36)(35,41);(19,24)(20,21)(23,25)(26,28)(27,32)(29,37)(30,38)(31,39)(33,36)(34,40)(35,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2031);