Finite Group DatabasebetaFinite Group Databasebeta| order | 1840 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C23 ⋊ Q16 |
| Sylow | C23 ⋊ #689 |
| Sylow | C5 ⋊ #67275 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11745065 |
| commutator, Fitting, cosocle | C4×C5×C23 | C22 |
| Frattini, hypercenter | C4 | D5×D23 |
| socle, prime radical | C2×C5×C23 | D4 |
| hypocenter | C5×C23 | Q16 |
| LCS | G ▷ C4×C5×C23 ▷ C2×C5×C23 ▷ C5×C23 | |
| UCS | C1 ◁ C2 ◁ C4 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 1840 |
Polycyclic presentation:
2^4,5,23|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,f^a=f^22,c^b=cd,e^b=e^4160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1840, 22);