Finite Group DatabasebetaFinite Group Databasebeta| order | 27450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | C3⋊(C3⋊(C5⋊D305)) |
| unambiguous semidirect product | C5⋊(C3⋊D915) |
| unambiguous semidirect product | C61⋊(C3⋊(C3⋊(C5⋊D5))) |
| Fitting, socle, derived, Hall | C32×C52×C61 ⋊ C2 |
| Hall | C52×C61 ⋊ C3⋊D3 |
| Hall | C32×C61 ⋊ C5⋊D5 |
| Hall | C32×C52 ⋊ D61 |
| Sylow | C61 ⋊ C3⋊(C3⋊(C5⋊D5)) |
| Sylow | C52 ⋊ C3⋊D183 |
| Sylow | C32 ⋊ C5⋊D305 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C52×C61 | C2 |
| LCS | G ▷ C32×C52×C61 | |
| UCS | C1 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13725 |
Polycyclic presentation:
2,3^2,5^2,61|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^606864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27450, 164);