Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12790 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | #432 |
| prime radical | C24×C13 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#97 ◁ G | |
450 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,22,28,23,27,37,42,24,26,36,41,21,34,35,47)(20,29,31,44,32,39,46,48,33,43,45,49,30,25,38,40);(14,15,16,17)(18,20,21,30,24,33,23,32)(19,25,27,29,26,39,34,43)(22,31,35,38,36,45,37,46)(28,40,42,44,41,48,47,49);(19,26)(22,36)(25,39)(27,34)(29,43)(31,45)(35,37)(38,46)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5778);