Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C541 ⋊ C2 |
| Sylow | C541 ⋊ #418 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^6,541|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^540,c^b=cf,d^b=df,g^b=g^5405422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 555);