Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #349×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1320 |
128 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 33 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,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,d^b=de,h^b=h^66,d^c=dg752 conjugacy classes — view the full character table.
| maximal subgroup of | #1320×D67, C2×#22558144, #30764951, … |
| maximal normal subgroup of | #1320×D67, C2×#22558144, #30764951, … |
| maximal quotient of | #30742449, #30742451, #30742461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2445);