Finite Group DatabasebetaFinite Group Databasebeta| order | 20288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×D4×C317 ⋊ C2 |
| Sylow | C317 ⋊ #459 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10144 |
Polycyclic presentation:
2^6,317|b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^316,e^c=ef3179 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20288, 744);