Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C61 · Schur multiplier (H2) = C2 |
| direct product | C22×C61×C7⋊C9 |
| derived, Sylow | C7 ⋊ C22×C9×C61 |
| Hall | C22×C7×C61 ⋊ C9 |
| Hall | C7×C61 ⋊ C22×C9 |
| Hall | C22×C7 ⋊ C9×C61 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15372 |
3660 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 62);