Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2258 |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,d^2=e,e^2=f,f^2=g,c^b=cg,h^c=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35292216, #35292218, #35324966, … |
| maximal normal subgroup of | #35292216, #35292218, #35324966, … |
| maximal quotient of | #35324582, #35324583, #35324599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6803);