Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#11718496 |
| Fitting | C2×C13×C4⋊C8 ⋊ C2 |
| Sylow | C13 ⋊ C2×#432 |
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15752386, #15752389, #15752397, … |
| maximal normal subgroup of | #15752386, #15752389, #15752397, … |
| maximal quotient of | C2×#13114583, C2×#13114597, C2×#13114691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13130);