Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #340×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1808 |
336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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=f,b^2=dg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^66,h^c=h^66968 conjugacy classes — view the full character table.
| maximal subgroup of | #30766901, #30766905, #30766917, … |
| maximal normal subgroup of | #30766901, #30766905, #30766917, … |
| maximal quotient of | #30748669, #30748682, #30748728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4538);