Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | C3⋊(C3⋊(C5⋊D115)) |
| unambiguous semidirect product | C5⋊(C3⋊D345) |
| unambiguous semidirect product | C23⋊(C3⋊(C3⋊(C5⋊D5))) |
| Fitting, socle, derived, Hall | C32×C52×C23 ⋊ C2 |
| Hall | C52×C23 ⋊ C3⋊D3 |
| Hall | C32×C52 ⋊ D23 |
| Hall | C32×C23 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C3⋊D69 |
| Sylow | C23 ⋊ C3⋊(C3⋊(C5⋊D5)) |
| Sylow | C32 ⋊ C5⋊D115 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C52×C23 | C2 |
| LCS | G ▷ C32×C52×C23 | |
| UCS | C1 | |
192 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5^2,23|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^222589 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×D345, D3×C3⋊(C5⋊D115), D69×C3⋊(C5⋊D5), … |
| maximal normal subgroup of | D15×D345, D3×C3⋊(C5⋊D115), D69×C3⋊(C5⋊D5), … |
| maximal quotient of | C3⋊(C3⋊(C23⋊#1039)), C2×C3⋊(C3⋊(C5⋊D115)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 52);