Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #2016 |
370 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 99 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=g,b^2=g,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^66,c^b=cf,d^b=dg,e^b=eg,h^b=h^66,d^c=dg,e^c=eg,h^c=h^661352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30744655, #30744656, #30744661, … |
| maximal normal subgroup of | #30744655, #30744656, #30744661, … |
| maximal quotient of | #30756331, #30756345, #30756393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5612);