Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#19128050 |
| Sylow | C83 ⋊ C2×#487 |
424 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19128050, #35412377, #35412422, … |
| maximal normal subgroup of | C4×#19128050, #35412377, #35412422, … |
| maximal quotient of | C2×#24907589, C2×#24908136, C2×#24908137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14819);