Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1288 |
152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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=d,b^2=e,c^2=fg,e^2=g,b^a=bc,c^a=cf,e^a=efg,h^a=h^66,d^b=dg1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1288×D67, C2×#22558074, #30745673, … |
| maximal normal subgroup of | #1288×D67, C2×#22558074, #30745673, … |
| maximal quotient of | #30742367, #30742377, #30742380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2375);