Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C4×#41×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3428 |
1540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^d=h^821708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35402131, #35402134, #35403949, … |
| maximal normal subgroup of | #35402131, #35402134, #35403949, … |
| maximal quotient of | #35562616, #35562631, #35562633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17709);