Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C8×#4343 |
| Fitting | C8×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C8×#41 |
456 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14663604, #14663614, #14663644, … |
| maximal normal subgroup of | #14663604, #14663614, #14663644, … |
| maximal quotient of | C8×#66945, C8×#66946, C8×Q8×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13468);