Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | Q8×C4⋊Dic13 |
| Sylow | C13 ⋊ Q8×C4⋊C4 |
568 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 333 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15757091, #15757095, #15757119, … |
| maximal normal subgroup of | #15757091, #15757095, #15757119, … |
| maximal quotient of | C4⋊C4×C4⋊Dic13, Q8×#88071, #15784465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7426);