Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#15692947 |
| Fitting | C2×M16×C103 ⋊ C2 |
| Sylow | C103 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27194948, C4×#15692947, #27194953, … |
| maximal normal subgroup of | #27194948, C4×#15692947, #27194953, … |
| maximal quotient of | C2×#20267518, C2×#20267521, #27193524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 561);