Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1330 |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,c^b=ceg,d^b=dg,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1330×D67, C2×#22558166, #30765548, … |
| maximal normal subgroup of | #1330×D67, C2×#22558166, #30765548, … |
| maximal quotient of | #30742491, #30742494, #30742497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2467);