Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | #108×#261 |
| Fitting | C13×#108 ⋊ C4 |
| Sylow | C13 ⋊ C4×#108 |
228 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 92 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×#359, #16789504, #261×#361, … |
| maximal normal subgroup of | #261×#359, #16789504, #261×#361, … |
| maximal quotient of | #261×#334, #261×#335, #16780917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20329);