Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3002 |
764 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^66,e^b=eg,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30750939, #30750941, #30827939, … |
| maximal normal subgroup of | #30750939, #30750941, #30827939, … |
| maximal quotient of | #30827941, #30827992, #30828043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13732);