Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D8×D332 |
| Fitting | C4×D8×C83 ⋊ C2 |
| Sylow | C83 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1183 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35317827, #35317831, #35317855, … |
| maximal normal subgroup of | #35317827, #35317831, #35317855, … |
| maximal quotient of | #35393756, #35393771, #35393786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16186);