Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#88148 |
| Fitting | C22×C13×C4⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ C22×#123 |
1968 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 605 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 | #15754266, #15755541, #15755557, … |
| maximal normal subgroup of | #15754266, #15755541, #15755557, … |
| maximal quotient of | C22×#11718325, C22×#11718650, C22×#11718326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17745);