Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16813642 |
| Fitting | C2×#41×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×#135 |
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390898, #28390899, #28390901, … |
| maximal normal subgroup of | #28390898, #28390899, #28390901, … |
| maximal quotient of | C2×#20298592, C2×#20298594, C2×#20298634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1329);