Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D1328 |
| Fitting | C4×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291853, #35291855, #35291859, … |
| maximal normal subgroup of | #35291853, #35291855, #35291859, … |
| maximal quotient of | C8×D1328, #35316301, #35316384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6358);