Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q64×D83 |
| Fitting | Q64×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×Q64 |
104 conjugacy classes of subgroups.
817 conjugacy classes — view the full character table.
| maximal subgroup of | SD128×D83, Q128×D83, #35325465, … |
| maximal normal subgroup of | SD128×D83, Q128×D83, #35325465, … |
| maximal quotient of | #1416×D83, #1423×D83, #35324987, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6813);