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.
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^b=h^82,h^c=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35324982, #35324986, #35324987, … |
| maximal normal subgroup of | #35324982, #35324986, #35324987, … |
| maximal quotient of | #35316137, #35316319, #35316394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6368);