Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×C83⋊#338 |
| unambiguous semidirect product | (C2×C83)⋊#338 |
| Sylow | C83 ⋊ C2×#338 |
372 conjugacy classes of subgroups.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291538, #35291540, #35291544, … |
| maximal normal subgroup of | #35291538, #35291540, #35291544, … |
| maximal quotient of | C2×#24905293, C2×#24905294, #35293822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4213);