Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C23⋊((C5⋊D5)⋊C3)) |
| unambiguous semidirect product | C23⋊(C3⋊((C5⋊D5)⋊C3)) |
| unambiguous semidirect product | (C3⋊(C5⋊D115))⋊C3 |
| Fitting, socle, derived | C3×C52×C23 ⋊ C2×C3 |
| Hall | C3×C23×C52⋊C3 ⋊ C2 |
| Hall | C52×C23 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ D23 |
| Sylow | C52 ⋊ C3×D69 |
| Sylow | C23 ⋊ C3⋊((C5⋊D5)⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C23 | C2×C3 |
| LCS | G ▷ C3×C52×C23 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5^2,23|c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^22,d^b=de,e^b=d^2e^3384 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D69, #35208101, D23×C3⋊((C5⋊D5)⋊C3), … |
| maximal normal subgroup of | #3874⋊D69, #35208101, D23×C3⋊((C5⋊D5)⋊C3), … |
| maximal quotient of | C3⋊(C23⋊(#1039⋊C3)), C2×C3⋊(C23⋊((C5⋊D5)⋊C3)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 48);