Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | AGL(1,ℤ/8)×Dic83 |
| Sylow | C83 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #453×Dic83, #35410281, #454×Dic83, … |
| maximal normal subgroup of | #453×Dic83, #35410281, #454×Dic83, … |
| maximal quotient of | AGL(1,ℤ/8)×C83⋊C8, #35373989, #35374012, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13320);