Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #469×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3058 |
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,h^b=h^66,d^c=dg,h^d=h^66560 conjugacy classes — view the full character table.
| maximal subgroup of | #30766823, #30766831, #31009731, … |
| maximal normal subgroup of | #30766823, #30766831, #31009731, … |
| maximal quotient of | #30838900, #30838939, #30838987, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14156);