Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D83)⋊C16 |
| Fitting | C22⋊C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,h^c=h^821720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×C16×D83, C2×(C22⋊D83)⋊C16, #35557571, … |
| maximal normal subgroup of | D4×C16×D83, C2×(C22⋊D83)⋊C16, #35557571, … |
| maximal quotient of | #35316106, #35316167, #35316173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6327);