Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×Dic13 |
| Sylow | C13 ⋊ C4×C4⋊Q8 |
588 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 289 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | Dic13×#333, Dic13×#332, #15753878, … |
| maximal normal subgroup of | Dic13×#333, Dic13×#332, #15753878, … |
| maximal quotient of | Dic13×#389, Dic13×#391, Dic13×#384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7083);