Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#137×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3278 |
482 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,h^c=h^66,e^d=eg755 conjugacy classes — view the full character table.
| maximal subgroup of | #3278×D67, C2×#22571869, #31731006, … |
| maximal normal subgroup of | #3278×D67, C2×#22571869, #31731006, … |
| maximal quotient of | #30847158, #30847274, #30847280, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16170);