Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | C4×C22⋊C4×D83 |
| Fitting | C4×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C4×C22⋊C4 |
1360 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1282×D83, #35294074, #1284×D83, … |
| maximal normal subgroup of | #1282×D83, #35294074, #1284×D83, … |
| maximal quotient of | C4×#95×D83, C4×#19127548, C4×C22⋊C4×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6838);