Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C32×C71 ⋊ C2 |
| Sylow | C71 ⋊ SD64 |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^6,71|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^70,c^b=cd,d^b=de,e^b=ef,g^b=g^701139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 388);