Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19127653 |
| Fitting | C2×#97×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C4×M16 |
656 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 341 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35293821, #35293827, #35294033, … |
| maximal normal subgroup of | #35293821, #35293827, #35294033, … |
| maximal quotient of | C2×#24905742, C2×#24905751, C2×#24905759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12918);