Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19128072 |
| Fitting | C22×SD16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#492 |
656 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19128072, #35412822, #35412869, … |
| maximal normal subgroup of | C4×#19128072, #35412822, #35412869, … |
| maximal quotient of | C2×#24907049, C2×#24907051, C2×#24907053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14915);