Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C16×C541 ⋊ C2 |
| Sylow | C541 ⋊ #359 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
Polycyclic presentation:
2^6,541|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^540,c^b=ce,e^b=ef,g^b=g^5408662 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 357);