Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q32×Dic83 |
| Sylow | C83 ⋊ C4×Q32 |
150 conjugacy classes of subgroups.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #35324980, SD64×Dic83, #35324987, … |
| maximal normal subgroup of | #35324980, SD64×Dic83, #35324987, … |
| maximal quotient of | Q32×C83⋊C8, #35316321, #35316395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6369);