Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#8999 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #120 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C22×D4×C13 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
530 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
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)(19,22,23,25)(26,27,30,34,31,35,29,33)(28,36,38,32,39,40,37,41);(14,15,16,17)(20,24)(22,25)(26,28)(27,32)(29,38)(30,37)(31,39)(33,40)(34,36)(35,41);(18,19)(20,25)(21,23)(22,24)(26,28)(27,32)(29,37)(30,38)(31,39)(33,36)(34,40)(35,41)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1987);