Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#41×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3461 |
1012 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^c=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295816, #35295819, #35370989, … |
| maximal normal subgroup of | #35295816, #35295819, #35370989, … |
| maximal quotient of | #35563095, #35563103, #35563111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17937);