Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #3407 |
360 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,e^2=f,f^2=g,d^a=dg,h^a=h^82,c^b=cg1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319532, #35319534, #35320563, … |
| maximal normal subgroup of | #35319532, #35319534, #35320563, … |
| maximal quotient of | #35557045, #35557054, #35557082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17613);