Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×C13×D7 |
| Fitting | C2×C4×C7×C13 ⋊ C2 |
| derived, Sylow | C7 ⋊ C22×C4×C13 |
| Hall | C7×C13 ⋊ C22×C4 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 728 |
520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 147);