Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13122 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C2×D4 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C8×D4 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ C22×C13×C16 ◁ G | |
326 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)(15,16)(18,19,24,29,25,28,43,46,22,27,31,32,23,40,42,48)(20,30,35,47,36,41,45,49,33,21,37,39,34,38,26,44);(14,15,17,16)(18,20,31,37,25,36,42,26,22,33,24,35,23,34,43,45)(19,21,32,47,28,38,48,49,27,30,29,39,40,41,46,44);(14,16,17,15)(18,21,22,30)(19,26,27,45)(20,32,33,29)(23,41,25,38)(24,39,31,47)(28,35,40,37)(34,46,36,48)(42,49,43,44)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6110);