Finite Group DatabasebetaFinite Group Databasebeta| order | 22540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(C49⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C49⋊(C23⋊AGL(1,𝔽5)) |
| Fitting, derived, Hall | C5×C23×C49 ⋊ C4 |
| Hall | C23×C49 ⋊ AGL(1,𝔽5) |
| Hall | C5×C49 ⋊ Dic23 |
| Hall | C5×C23 ⋊ Dic49 |
| Sylow | C49 ⋊ C23⋊AGL(1,𝔽5) |
| Sylow | C23 ⋊ C49⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic1127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C23×C49 | C4 |
| Frattini | C7 | C7⋊(C23⋊AGL(1,𝔽5)) |
| socle | C5×C7×C23 | Dic7 |
| prime radical | C7×D5×C23 | D7 |
| cosocle | D5×C23×C49 | C2 |
| LCS | G ▷ C5×C23×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5635 |
Polycyclic presentation:
2^2,5,7,23,7|a^2=b,d^7=f^6,c^a=c^2,d^a=d^6f,e^a=e^22,f^a=f^6,c^b=c^42257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22540, 14);