Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#19127539 |
| Sylow | C83 ⋊ C2×SD64 |
112 conjugacy classes of subgroups.
940 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19127539, #35324986, #35324992, … |
| maximal normal subgroup of | C4×#19127539, #35324986, #35324992, … |
| maximal quotient of | C2×#24905641, C2×#24905643, C2×#24905664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6811);