Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#88123 |
| Sylow | C13 ⋊ C4×C4⋊Q8 |
588 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15750896, #15750898, #15750900, … |
| maximal normal subgroup of | #15750896, #15750898, #15750900, … |
| maximal quotient of | C4×#11718589, C4×#11718590, C4×#11718596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7082);