Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3162 |
348 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=e,c^2=f,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,c^b=cg1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30750784, #30756821, #30756822, … |
| maximal normal subgroup of | #30750784, #30756821, #30756822, … |
| maximal quotient of | #30856254, #30859184, #30860408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15034);