Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#25893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#550 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×D4×C13 ◁ G | |
1344 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19)(20,24)(21,23)(22,25)(26,27)(28,34)(29,40)(30,37)(31,36)(32,35)(33,39)(38,41);(18,20,22,21)(19,23,25,24)(26,28)(27,33)(29,32)(30,38)(31,39)(34,36)(35,41)(37,40);(14,15,16,17)(18,20,22,21)(19,24,25,23)(26,29,30,39,31,38,32,28)(27,34,35,41,36,33,37,40);(18,21,22,20)(19,24,25,23)(26,30,31,32)(27,35,36,37)(28,38,39,29)(33,41,34,40)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18881);