Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#19127616 |
| Fitting | C22×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#394 |
1252 conjugacy classes of subgroups.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35326194, C4×#19127616, #35329709, … |
| maximal normal subgroup of | #35326194, C4×#19127616, #35329709, … |
| maximal quotient of | C2×#24905702, C2×#24905706, C2×#24905707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7714);