Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C67 ⋊ #2946 |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=f,c^2=f,e^2=g,b^a=be,e^a=eg,h^a=h^66,e^b=eg,d^c=dg,h^c=h^66770 conjugacy classes — view the full character table.
| maximal subgroup of | #30876634, #30876638, #30876652, … |
| maximal normal subgroup of | #30876634, #30876638, #30876652, … |
| maximal quotient of | #30825270, #30825461, #30825482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13343);