Finite Group DatabasebetaFinite Group Databasebeta| order | 22540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D805 |
| unambiguous semidirect product | (C5×D7)⋊D161 |
| unambiguous semidirect product | (C7×D7)⋊D115 |
| unambiguous semidirect product | (D7×C23)⋊D35 |
| Fitting, socle, derived, Hall | C5×C72×C23 ⋊ C22 |
| Hall | C72×C23 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D23 |
| Hall | C5×C23 ⋊ D72 |
| Sylow | C72 ⋊ C2×D115 |
| Sylow | C23 ⋊ D7×D35 |
| Sylow | C5 ⋊ D7×D161 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C23 | C22 |
| LCS | G ▷ C5×C72×C23 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1610 |
2020 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22540, 65);