Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19127952 |
| Fitting | C2×#121×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#469 |
596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 596 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.
1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19127952, #35411045, #35411081, … |
| maximal normal subgroup of | C4×#19127952, #35411045, #35411081, … |
| maximal quotient of | C2×#24906940, C2×#24906974, C2×#24907022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14104);