Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C67 ⋊ #2245 |
132 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|a^2=g,b^2=eg,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,c^b=cg,h^c=h^66752 conjugacy classes — view the full character table.
| maximal subgroup of | #2245×D67, C2×#22562453, #31011151, … |
| maximal normal subgroup of | #2245×D67, C2×#22562453, #31011151, … |
| maximal quotient of | #30772215, #30773765, #30773766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6754);