Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C8×C509 ⋊ C4 |
| Sylow | C509 ⋊ H(3,ℤ/4) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8144 |
Polycyclic presentation:
2^6,509|a^2=d,b^2=e,c^2=f,b^a=bc,e^a=ef,g^a=g^208,d^b=df,g^b=g^301,g^d=g^508,g^e=g^5082054 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1417);