Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×#1055 |
| Sylow | C13 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15753476, #100×#1055, #15753481, … |
| maximal normal subgroup of | #15753476, #100×#1055, #15753481, … |
| maximal quotient of | #97×#1055, #15752300, #15753344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2788);