Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34509 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#553 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(19,22)(20,24)(27,31)(28,34)(33,38)(35,40);(18,19,21,22)(20,23,24,25)(27,31)(32,37)(33,38)(39,41);(18,19)(20,23)(21,22)(24,25)(26,27,30,31)(28,32,34,37)(29,33,36,38)(35,39,40,41);(14,16,17,15)(18,19)(20,23)(21,22)(24,25)(26,28)(27,32)(29,35)(30,34)(31,37)(33,39)(36,40)(38,41);(18,20)(19,23)(21,24)(22,25)(26,29,30,36)(27,33,31,38)(28,35,34,40)(32,39,37,41)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27497);