Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×#13050579 |
| Fitting | C8×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ Q8×SD16 |
370 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 370 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.
1675 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35393896, #35393903, #35393956, … |
| maximal normal subgroup of | #35393896, #35393903, #35393956, … |
| maximal quotient of | Q8×#14581714, Q8×#14581717, C4⋊C4×#13050579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17371);