Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×Dic9⋊C4 |
| unambiguous semidirect product | Dic9⋊(C4×C7) |
| Hall | C7×C9 ⋊ C4⋊C4 |
| Sylow | C9 ⋊ C7×C4⋊C4 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 1008 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7)(8,13,15,14,9,11,10,16,12)(17,18,19,20)(22,24);(9,11)(10,14)(12,13)(15,16)(21,22,23,24)294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 82);