Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #444×D83 |
| Fitting | #444×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#444 |
464 conjugacy classes of subgroups.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #2180×D83, AGL(1,ℤ/16)×D83, #35557849, … |
| maximal normal subgroup of | #2180×D83, AGL(1,ℤ/16)×D83, #35557849, … |
| maximal quotient of | SD16⋊C8×D83, #1579×D83, #1580×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13402);