Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#88063 |
| Fitting | C22×C13×M16 ⋊ C2 |
| Sylow | C13 ⋊ C22×#100 |
992 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 269 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 | #15768235, #15768238, #15768280, … |
| maximal normal subgroup of | #15768235, #15768238, #15768280, … |
| maximal quotient of | C22×#11718060, C2×#13113156, C2×#13113162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12976);