Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×C22⋊(C7⋊C27) |
| unambiguous semidirect product | (C2×C7)⋊(C22⋊C27) |
| derived | C22×C7 ⋊ C2×C27 |
| Hall | C23×C7 ⋊ C27 |
| Sylow | C23 ⋊ C7⋊C27 |
| Sylow | C7 ⋊ C2×C22⋊C27 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 378 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 92);