Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#11718328 |
| Fitting | C2×C13×#95 ⋊ C2 |
| Sylow | C13 ⋊ C2×#380 |
1232 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 349 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 | #15752537, #15752921, #15752949, … |
| maximal normal subgroup of | #15752537, #15752921, #15752949, … |
| maximal quotient of | C2×#13113057, C2×#13113061, C2×#13113064, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6882);