Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C7×#638 |
| Fitting | C23×C32×C7 ⋊ C2 |
| Hall | C32×C7 ⋊ C2×D4 |
| Sylow | C32 ⋊ C2×C7×D4 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×D4×C3⋊D3, C2×D7×#638, C2×#11759581, … |
| maximal normal subgroup of | C2×C7×D4×C3⋊D3, C2×D7×#638, C2×#11759581, … |
| maximal quotient of | C7×#64149, C7×#64146, C7×#64162 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 865);