Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1353 |
116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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,d^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^66,c^b=cf,d^b=defg,d^c=dg749 conjugacy classes — view the full character table.
| maximal subgroup of | #1353×D67, C2×#22558236, #30766134, … |
| maximal normal subgroup of | #1353×D67, C2×#22558236, #30766134, … |
| maximal quotient of | #30742625, #30742651, #30742953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2537);