Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#10622604 |
| Fitting | C22×C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ C2×#394 |
1252 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 261 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
244 conjugacy classes — view the full character table.
| maximal subgroup of | #14648785, #14648787, #14648790, … |
| maximal normal subgroup of | #14648785, #14648787, #14648790, … |
| maximal quotient of | C2×#13066856, C2×#13066858, C2×#13066864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7716);