Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #137×Dic83 |
| Sylow | C83 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #455×Dic83, #35410292, #456×Dic83, … |
| maximal normal subgroup of | #455×Dic83, #35410292, #456×Dic83, … |
| maximal quotient of | #137×C83⋊C8, #35374000, #35374023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13331);