Finite Group DatabasebetaFinite Group Databasebeta| order | 1840 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C5×Q8×C23 ⋊ C2 |
| Hall | C5×C23 ⋊ SD16 |
| Sylow | C23 ⋊ #688 |
| Sylow | C5 ⋊ #67274 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 920 |
Polycyclic presentation:
2^4,5,23|b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^22,c^b=cd292 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1840, 77);