Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic22 |
| Hall | C3×C5×C11 ⋊ Q8 |
| Hall | C5×C11 ⋊ C3×Q8 |
| Hall | C3×C11 ⋊ C5×Q8 |
| Sylow | C11 ⋊ C3×C5×Q8 |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1320 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(13,16,15,14)(17,18,19,20,21,22,23,24,25,26,27);(9,13,11,15)(10,14,12,16)(18,27)(19,26)(20,25)(21,24)(22,23)375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 95);