Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D433⋊#101 |
| Sylow | C433 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6928 |
Polycyclic presentation:
2^6,433|a^2=e,b^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^179,e^b=ef,g^c=g^432,g^e=g^4321102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1534);