Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#19128054 |
| Sylow | C83 ⋊ C2×#488 |
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19128054, #35412392, #35412396, … |
| maximal normal subgroup of | C4×#19128054, #35412392, #35412396, … |
| maximal quotient of | C2×#24907592, C2×#24908137, C2×#24908140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14824);