Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #67355 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×#67356 |
| Fitting | C22×C7×C9 ⋊ C2×C3 |
| Hall | #4427 ⋊ C23 |
| Hall | C22×D7 ⋊ 3−1+2 |
| Sylow | C7 ⋊ C23×3−1+2 |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#67356⋊C2, C22×3−1+2×AGL(1,𝔽7) |
| maximal normal subgroup of | C22×#67356⋊C2, C22×3−1+2×AGL(1,𝔽7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 506);