Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D13×#358 |
| Fitting | C13×#358 ⋊ C2 |
| Sylow | C13 ⋊ C2×#358 |
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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 | C2×D13×#358, D13×#2138, D13×#2141, … |
| maximal normal subgroup of | C2×D13×#358, D13×#2138, D13×#2141, … |
| maximal quotient of | D13×#1332, #15772896, #15772948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6210);