Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#10622552 |
| Fitting | C22×C42×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#390 |
1360 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13066436, #14641757, #14641759, … |
| maximal normal subgroup of | C2×#13066436, #14641757, #14641759, … |
| maximal quotient of | C2×#13066846, C2×#13066854, C4×#10622552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6966);