Finite Group DatabasebetaFinite Group Databasebeta| order | 26176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C42×C409 ⋊ C4 |
| Sylow | C409 ⋊ #354 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6544 |
Polycyclic presentation:
2^6,409|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^143,c^b=cf,d^b=def,g^b=g^408,d^c=df,g^d=g^4081645 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26176, 1456);