Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M64×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2264 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^82,d^b=de,e^b=ef,f^b=fg,h^b=h^821666 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35325021, #35325024, #35325083, … |
| maximal normal subgroup of | #35325021, #35325024, #35325083, … |
| maximal quotient of | #35324844, #35324852, #35324911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6830);