Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#88172 |
| Fitting | C22×C13×Q16 ⋊ C2 |
| Sylow | C13 ⋊ C22×#137 |
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #15864283, #15864294, #15864319, … |
| maximal normal subgroup of | #15864283, #15864294, #15864319, … |
| maximal quotient of | C22×#11718463, C22×#11718464, C22×#11718542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19250);