Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1982 |
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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=dfg,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^66,d^b=dg,f^b=fg1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30747738, #30747743, #30747780, … |
| maximal normal subgroup of | #30747738, #30747743, #30747780, … |
| maximal quotient of | #30754787, #30754805, #30754874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5437);