Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×2−1+4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3013 |
712 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,e^b=eg,d^c=dg1426 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35435863, #35435867, #35435872, … |
| maximal normal subgroup of | #35435863, #35435867, #35435872, … |
| maximal quotient of | #35377619, #35377630, #35377707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13825);