Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×#88126 |
| Fitting | C43×C13 ⋊ C2 |
| Sylow | C13 ⋊ C4×#117 |
752 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 357 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 | #15752356, #15752362, #15752365, … |
| maximal normal subgroup of | #15752356, #15752362, #15752365, … |
| maximal quotient of | C4×#11718593, C42×#6103, C42×#6101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6852);