Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128275 |
| Fitting | C23×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#536 |
1512 conjugacy classes of subgroups.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35310934, #35310982, #35310997, … |
| maximal normal subgroup of | #35310934, #35310982, #35310997, … |
| maximal quotient of | C2×#24910049, C2×#24910056, C2×#24910087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17827);