Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of #87648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C7 |
| direct product | C4×C22⋊(C7⋊D7) |
| Fitting | C22×C4×C72 ⋊ C2 |
| Sylow | C72 ⋊ C4×D4 |
470 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 784 |
404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D4×C7⋊D7, C4×#11924217 |
| maximal normal subgroup of | C4×D4×C7⋊D7, C4×#11924217 |
| maximal quotient of | #72259541 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 734);