Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #123×Dic83 |
| Sylow | C83 ⋊ C4×#123 |
688 conjugacy classes of subgroups.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #352×Dic83, #35320370, #458×Dic83, … |
| maximal normal subgroup of | #352×Dic83, #35320370, #458×Dic83, … |
| maximal quotient of | #386×Dic83, #388×Dic83, #385×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7033);