Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#9658 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C2×D4 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle, prime radical | C23×C13 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G | |
486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
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)(18,19,21,24,22,20,23,25)(26,27)(28,36)(29,32)(30,39)(31,35)(33,37)(34,40)(38,41);(14,15,16,17)(18,20,21,25,22,19,23,24)(26,28,30,29,31,37,40,38)(27,32,34,36,35,41,39,33);(26,29,30,37,31,38,40,28)(27,33,34,32,35,36,39,41)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2646);