Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C8×#261 |
| Fitting | C13×C22⋊C8 ⋊ C4 |
| Sylow | C13 ⋊ C4×C22⋊C8 |
436 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#323, #261×#324, #16780373, … |
| maximal normal subgroup of | #261×#323, #261×#324, #16780373, … |
| maximal quotient of | C22⋊C8×#1057, #16780318, #16780320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20235);