Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #1296 |
188 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^66,c^b=cg1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1296×D67, C2×#22558093, #30745916, … |
| maximal normal subgroup of | #1296×D67, C2×#22558093, #30745916, … |
| maximal quotient of | #30742383, #30742399, #30742400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2394);