Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Fitting | C82×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1705 |
214 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=d,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^822662 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35318165, #1705×D83, C2×#24907050, … |
| maximal normal subgroup of | #35318165, #1705×D83, C2×#24907050, … |
| maximal quotient of | #35298171, #35304138, #35304144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4097);