Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#19128000 |
| Fitting | C2×#106×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#478 |
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19128000, #35412017, #35412082, … |
| maximal normal subgroup of | C4×#19128000, #35412017, #35412082, … |
| maximal quotient of | C2×#24907472, C2×#24907711, C2×#24907721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14266);