Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#6380 |
| Fitting | C72×C22⋊C4 ⋊ C2 |
| Sylow | C72 ⋊ #99 |
155 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 155 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 56 |
287 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#89804, #72215098, #72215149, … |
| maximal normal subgroup of | C7×#89804, #72215098, #72215149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 249);