Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#135×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3584 |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,d^c=dg,h^d=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35320108, #35320110, #35320113, … |
| maximal normal subgroup of | #35320108, #35320110, #35320113, … |
| maximal quotient of | #36267965, #36268079, #36268518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19279);