Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #336×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1270 |
202 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 61 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=d,c^2=f,d^2=g,b^a=bc,c^a=ce,c^b=cf,d^b=def,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1270×D67, C2×#22558029, #30743768, … |
| maximal normal subgroup of | #1270×D67, C2×#22558029, #30743768, … |
| maximal quotient of | #30742383, #30742574, #30742576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2330);