Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#22639 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C23×C4 |
| prime radical | C24×C13 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
828 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(20,21)(22,23)(24,26)(25,27)(28,29)(30,31,32,34,33,35,36,37);(14,15,18,19)(16,20,17,21)(22,24,25,28)(23,26,27,29);(14,16,18,17)(15,20,19,21)(23,27)(26,29);(14,17,18,16)(15,20,19,21)1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15627);