Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M64×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2264 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|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^66,d^b=de,e^b=ef,f^b=fg,h^b=h^661346 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30776448, #30776451, #30776510, … |
| maximal normal subgroup of | #30776448, #30776451, #30776510, … |
| maximal quotient of | #30776271, #30776279, #30776338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6830);