Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26799 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C22⋊C4 ◁ G | |
854 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)(15,16)(18,19)(20,25)(21,23)(22,24)(26,27,29,32)(28,34,36,31)(30,33,38,40)(35,39,37,41);(14,15,17,16)(18,20,22,21)(19,23,24,25)(26,28)(27,31)(29,36)(30,35)(32,34)(33,41)(37,38)(39,40);(14,15,17,16)(18,21,22,20)(19,23,24,25)(27,32)(28,35)(30,38)(31,39)(34,41)(36,37);(14,16,17,15)(19,24)(23,25)(27,32)(31,34)(33,40)(39,41)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19787);