Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128466 |
| Fitting | C2×#131×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#568 |
1460 conjugacy classes of subgroups.
1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319859, #35402106, #35402255, … |
| maximal normal subgroup of | #35319859, #35402106, #35402255, … |
| maximal quotient of | C2×#24915879, C2×#24915889, C2×#24915890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19218);