Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2178 |
146 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 61 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,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^82,d^b=df,f^b=fg,h^c=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35325009, #35325012, #35325014, … |
| maximal normal subgroup of | #35325009, #35325012, #35325014, … |
| maximal quotient of | D16×C83⋊C8, SD32×C83⋊C8, Q32×C83⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6391);