Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#12657 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×C42 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C2×#97 |
| prime radical | C23×C13 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ G | |
334 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)(14,15,16,17)(18,19)(20,30,33,45)(21,26)(22,27)(23,38)(24,29)(25,32,41,46)(28,39)(31,42,34,48)(35,49,47,40)(36,43)(37,44);(15,17)(18,20,23,34,22,32,36,47,24,33,39,31,37,46,21,35)(19,25,28,40,27,30,26,42,29,41,38,49,44,45,43,48);(18,21,22,23,24,36,37,39)(19,26,27,38,29,43,44,28)(20,31,46,47,33,34,32,35)(25,40,45,48,41,49,30,42)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5645);