Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #1883 |
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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=dfg,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^66,d^b=dg,f^b=fg,h^b=h^66,e^c=eg758 conjugacy classes — view the full character table.
| maximal subgroup of | #1883×D67, C2×#22560587, #30857336, … |
| maximal normal subgroup of | #1883×D67, C2×#22560587, #30857336, … |
| maximal quotient of | #30750457, #30750471, #30750538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4888);