Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#11718106 |
| Fitting | C2×C13×M32 ⋊ C2 |
| Sylow | C13 ⋊ C2×#349 |
236 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
284 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15777958, C4×#11718106, #15777962, … |
| maximal normal subgroup of | #15777958, C4×#11718106, #15777962, … |
| maximal quotient of | C2×#13112759, #15771980, C2×#13112775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6127);