Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1572 |
150 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 73 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=d,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cg,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1572×D67, C2×#22558987, #30824902, … |
| maximal normal subgroup of | #1572×D67, C2×#22558987, #30824902, … |
| maximal quotient of | #30745310, #30747039, #30747044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3288);