Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10623101 |
| Sylow | C11 ⋊ C2×#557 |
1048 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 581 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14645510, #14645519, #14645522, … |
| maximal normal subgroup of | #14645510, #14645519, #14645522, … |
| maximal quotient of | C2×Q8×C4⋊Dic11, C2×#13071534, C2×#13071571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18083);