Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#11718117 |
| Sylow | C13 ⋊ C2×#323 |
456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
284 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15749877, #15749878, #15750038, … |
| maximal normal subgroup of | #15749877, #15749878, #15750038, … |
| maximal quotient of | C2×#13112657, C2×#13112662, #15750871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2817);