Finite Group DatabasebetaFinite Group Databasebeta| order | 30545 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C149 · Schur multiplier (H2) = C1 |
| direct product | C149×C41⋊C5 |
| unambiguous semidirect product | C41⋊(C5×C149) |
| unambiguous semidirect product | (C41×C149)⋊C5 |
| Fitting, socle, Hall | C41×C149 ⋊ C5 |
| derived, Sylow | C41 ⋊ C5×C149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C149 | C41⋊C5 |
| commutator, cosocle, hypocenter | C41 | C5×C149 |
| Frattini | C1 | G |
| Fitting, socle | C41×C149 | C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C149 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6109 |
1937 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30545, 1);