Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #542×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3124 |
384 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #3124×D67, C2×#22570465, #31724193, … |
| maximal normal subgroup of | #3124×D67, C2×#22570465, #31724193, … |
| maximal quotient of | #30855935, #30858901, #30858946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14766);