Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M16×C541 ⋊ C2 |
| Sylow | C541 ⋊ #408 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
Polycyclic presentation:
2^6,541|a^2=e,e^2=f,b^a=bd,g^a=g^540,c^b=cf,g^b=g^5405428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 517);