Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | #97×#261 |
| Fitting | C13×#97 ⋊ C4 |
| Sylow | C13 ⋊ C4×#97 |
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#329, #261×#330, #16780697, … |
| maximal normal subgroup of | #261×#329, #261×#330, #16780697, … |
| maximal quotient of | #261×#322, #97×#1057, #16778862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20163);