Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C67 ⋊ C4×#101 |
296 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 107 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=f,c^2=eg,f^2=g,b^a=bd,f^a=fg,d^b=dg,h^c=h^66770 conjugacy classes — view the full character table.
| maximal subgroup of | #30766197, #30766199, #30766207, … |
| maximal normal subgroup of | #30766197, #30766199, #30766207, … |
| maximal quotient of | #30746336, #30746344, #30746348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4305);