Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#121×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1999 |
496 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|d^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cf,d^b=dg,h^b=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #1999×D67, C2×#22561205, #30882633, … |
| maximal normal subgroup of | #1999×D67, C2×#22561205, #30882633, … |
| maximal quotient of | #30756025, #30756027, #30756032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5506);