Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#88126 |
| Fitting | C22×C42×C13 ⋊ C2 |
| Sylow | C13 ⋊ C22×#117 |
1880 conjugacy classes of subgroups; only the 901 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 901 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15754251, #15768138, #15768163, … |
| maximal normal subgroup of | #15754251, #15768138, #15768163, … |
| maximal quotient of | C22×#11718593, C22×C4×#6103, C22×C4×#6101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17674);