Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #6118 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#88106 |
| Sylow | C13 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16777087, #16777089, #16777091, … |
| maximal normal subgroup of | #16777087, #16777089, #16777091, … |
| maximal quotient of | C8×#88106, #16786599, #16786644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20714);