Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2020 |
342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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=g,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,f^b=fg,h^b=h^66,d^c=dg,e^c=eg,f^c=fg950 conjugacy classes — view the full character table.
| maximal subgroup of | #30767977, #30767982, #30767987, … |
| maximal normal subgroup of | #30767977, #30767982, #30767987, … |
| maximal quotient of | #30756441, #30756458, #30756513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5629);