Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3368 |
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^66,f^c=fg953 conjugacy classes — view the full character table.
| maximal subgroup of | #30845778, #30845780, #30845838, … |
| maximal normal subgroup of | #30845778, #30845780, #30845838, … |
| maximal quotient of | #30872476, #30872665, #30874795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17237);