Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#11719142 |
| Fitting | C22×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ C2×#410 |
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #16785348, #16785353, #16785378, … |
| maximal normal subgroup of | #16785348, #16785353, #16785378, … |
| maximal quotient of | C2×#13130068, C2×#13130076, C2×#13130080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21107);