Finite Group DatabasebetaFinite Group Databasebeta| order | 18860 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#11717961 |
| Fitting, socle, derived, Hall | C5×C23×C41 ⋊ C4 |
| Hall | C23×C41 ⋊ AGL(1,𝔽5) |
| Hall | C5×C41 ⋊ Dic23 |
| Hall | C5×C23 ⋊ #4223 |
| Sylow | C41 ⋊ C23⋊AGL(1,𝔽5) |
| Sylow | C23 ⋊ #11717961 |
| Sylow | C5 ⋊ C23⋊#4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C23×C41 | C4 |
| prime radical, cosocle | C23×D205 | C2 |
| LCS | G ▷ C5×C23×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4715 |
Polycyclic presentation:
2^2,5,23,41|a^2=b,c^a=c^2,d^a=d^22,e^a=e^32,c^b=c^4,e^b=e^401199 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18860, 29);