Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#7932 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C13 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | C2×#95 |
| prime radical | C24×C13 | C42 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C13 ◁ C22×C42×C13 ◁ G | |
666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20,19,21,18,16)(22,23)(24,32,34,28)(25,29)(26,31)(27,30)(33,37,35,36);(14,16,18,21,19,20,17,15)(22,24,26,35,27,34,25,33)(23,28,31,37,30,32,29,36);(22,25,27,26)(23,29,30,31)(24,33,34,35)(28,36,32,37)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 920);