Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | #126×Dic13 |
| Sylow | C13 ⋊ C4×#126 |
516 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D13×#126, C2×#126×Dic13, C4×#11719411, … |
| maximal normal subgroup of | C4×D13×#126, C2×#126×Dic13, C4×#11719411, … |
| maximal quotient of | Dic13×#388, Dic13×#387, Dic13×#383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7062);