Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×C4×(C2×D83)⋊C4 |
| Fitting | C22×C42×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C4×C22⋊C4 |
1360 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19127424, #35294915, #35297058, … |
| maximal normal subgroup of | C4×#19127424, #35294915, #35297058, … |
| maximal quotient of | C2×C4×C83⋊#95, C42×(C2×D83)⋊C4, C2×(C2×D83)⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6841);