Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C509 ⋊ C4 |
| Sylow | C509 ⋊ #353 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4072 |
Polycyclic presentation:
2^6,509|a^2=d,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^301,c^b=cf,d^b=def,g^b=g^508,d^c=df,g^d=g^5082045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1454);