Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #127×#261 |
| Fitting | C13×#127 ⋊ C4 |
| Sylow | C13 ⋊ C4×#127 |
924 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#331, #16780714, #16780723, … |
| maximal normal subgroup of | #261×#331, #16780714, #16780723, … |
| maximal quotient of | #261×#390, #261×#384, #261×#392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20980);