Finite Group DatabasebetaFinite Group Databasebeta| order | 22540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D115⋊D49 |
| unambiguous semidirect product | D245⋊D23 |
| unambiguous semidirect product | D1127⋊D5 |
| Fitting, derived, Hall | C5×C23×C49 ⋊ C22 |
| Hall | C23×C49 ⋊ C2×D5 |
| Hall | C5×C49 ⋊ C2×D23 |
| Hall | C5×C23 ⋊ C2×D49 |
| Sylow | C49 ⋊ D5×D23 |
| Sylow | C23 ⋊ D5×D49 |
| Sylow | C5 ⋊ D23×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C23×C49 | C22 |
| Frattini | C7 | D35⋊D23 |
| socle | C5×C7×C23 | C2×D7 |
| LCS | G ▷ C5×C23×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5635 |
Polycyclic presentation:
2^2,5,7,23,7|d^7=f^6,d^a=d^6f,e^a=e^22,f^a=f^6,c^b=c^4,d^b=d^6f,f^b=f^61468 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22540, 20);