Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C67 ⋊ #2912 |
476 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 293 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=e,e^2=g,b^a=be,e^a=eg,h^a=h^66,d^c=dg1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30772146, #30772150, #30772151, … |
| maximal normal subgroup of | #30772146, #30772150, #30772151, … |
| maximal quotient of | #30824820, #30824874, #30824958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13105);