Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C8×C433 ⋊ C4 |
| Sylow | C433 ⋊ #340 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6928 |
Polycyclic presentation:
2^6,433|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^179,g^d=g^4321756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1423);