Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#19128108 |
| Sylow | C83 ⋊ C2×#501 |
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19128108, #35413215, #35413223, … |
| maximal normal subgroup of | C4×#19128108, #35413215, #35413223, … |
| maximal quotient of | C2×#24907628, C2×#24908199, C2×#24908200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15027);