Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16813654 |
| Fitting | C2×Q16×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
806 conjugacy classes — view the full character table.
| maximal subgroup of | #28399390, C4×#16813654, #28399412, … |
| maximal normal subgroup of | #28399390, C4×#16813654, #28399412, … |
| maximal quotient of | C2×#20298605, C2×#20298598, C2×#20298639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1343);