Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2248 |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=dfg,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^822662 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35317844, #35317845, #35317851, … |
| maximal normal subgroup of | #35317844, #35317845, #35317851, … |
| maximal quotient of | #35319067, #35319090, #35319094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6766);