Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×AGL(1,ℤ/8)×D83 |
| Fitting | C2×AGL(1,ℤ/8)×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×AGL(1,ℤ/8) |
1720 conjugacy classes of subgroups.
946 conjugacy classes — view the full character table.
| maximal subgroup of | #1883×D83, #35405932, #1903×D83, … |
| maximal normal subgroup of | #1883×D83, #35405932, #1903×D83, … |
| maximal quotient of | C2×#418×D83, C2×#417×D83, C2×#428×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19240);