Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128274 |
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#536 |
1512 conjugacy classes of subgroups.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296913, #35405655, #35405657, … |
| maximal normal subgroup of | #35296913, #35405655, #35405657, … |
| maximal quotient of | C2×#24910046, C2×#24910052, C2×#24910085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17826);