Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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,b^2=g,c^2=eg,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,d^b=df,f^b=fg,h^c=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Q32×D83, C2×#24909319, #35557682, … |
| maximal normal subgroup of | C4×Q32×D83, C2×#24909319, #35557682, … |
| maximal quotient of | #35316135, #35316317, #35316323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6366);