Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1542 |
212 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 89 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=e,b^2=g,c^2=f,d^2=g,e^2=fg,b^a=bd,d^a=df,h^a=h^66,d^b=dg,e^b=efg,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30746902, #30746907, #30746916, … |
| maximal normal subgroup of | #30746902, #30746907, #30746916, … |
| maximal quotient of | #30743779, #30743793, #30744125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3168);