Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3100 |
492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^66,f^c=fg962 conjugacy classes — view the full character table.
| maximal subgroup of | #30825694, #30825696, #30825763, … |
| maximal normal subgroup of | #30825694, #30825696, #30825763, … |
| maximal quotient of | #30855827, #30858755, #30858757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14508);