Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#14581737 |
| Fitting | C22×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×SD32 |
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35321467, #35321469, #35321474, … |
| maximal normal subgroup of | #35321467, #35321469, #35321474, … |
| maximal quotient of | C22×#19127503, C22×#19127506, C22×#19127529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17620);