Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #6118 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C8×C22⋊#261 |
| Fitting | C22×C8×C13 ⋊ C4 |
| Sylow | C13 ⋊ C8×C22⋊C4 |
384 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16777278, #16777279, #16777290, … |
| maximal normal subgroup of | #16777278, #16777279, #16777290, … |
| maximal quotient of | C8×C22⋊#1057, C8×#88111, #16780323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20242);