Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D11×#349 |
| Fitting | C11×#349 ⋊ C2 |
| Sylow | C11 ⋊ C2×#349 |
236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1320, #14662893, D11×#1321, … |
| maximal normal subgroup of | D11×#1320, #14662893, D11×#1321, … |
| maximal quotient of | D11×#1314, #14662833, D11×#1322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6126);