Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#88201 |
| Fitting | C23×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ C22×#124 |
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15755554, #15769460, #15769463, … |
| maximal normal subgroup of | #15755554, #15769460, #15769463, … |
| maximal quotient of | C22×#11718638, C22×#11718651, C22×#11718649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17759);