Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #546×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3275 |
498 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,h^b=h^66,e^d=eg854 conjugacy classes — view the full character table.
| maximal subgroup of | #3275×D67, C2×#22571836, #31731007, … |
| maximal normal subgroup of | #3275×D67, C2×#22571836, #31731007, … |
| maximal quotient of | #30847125, #30847216, #30847231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16137);