Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C4×#13050573 |
| Fitting | C2×C4×C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C4×M16 |
656 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 357 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35293784, #35293791, #35293796, … |
| maximal normal subgroup of | #35293784, #35293791, #35293796, … |
| maximal quotient of | C2×C8×#13050573, C2×#24905749, C2×#24905757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12916);