Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #2004 |
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|b^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,c^b=cf,d^b=dg,h^b=h^66,d^c=dg752 conjugacy classes — view the full character table.
| maximal subgroup of | #2004×D67, C2×#22561236, #30882735, … |
| maximal normal subgroup of | #2004×D67, C2×#22561236, #30882735, … |
| maximal quotient of | #30756039, #30756053, #30756095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5537);