Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D11×#100 |
| Fitting | C2×C11×#100 ⋊ C2 |
| Sylow | C11 ⋊ C22×#100 |
992 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 221 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×#1390, #14668718, #14671249, … |
| maximal normal subgroup of | D11×#1390, #14668718, #14671249, … |
| maximal quotient of | C2×D11×#323, D11×#1460, C2×#13066935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12975);