Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×C23⋊#3874 |
| unambiguous semidirect product | C23⋊(C3×#3874) |
| Fitting, socle | C3×C52×C23 ⋊ D3 |
| derived | C23×C52⋊C3 ⋊ 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×#3874 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C23⋊#3874 |
| commutator, cosocle, hypocenter | C23×C52⋊C3 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C23 | D3 |
| LCS | G ▷ C23×C52⋊C3 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
402 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#3874⋊D23, C3×((C5⋊D5)⋊C3)⋊D23, C3×D23×#3874, … |
| maximal normal subgroup of | C3×#3874⋊D23, C3×((C5⋊D5)⋊C3)⋊D23, C3×D23×#3874, … |
| maximal quotient of | C3×C23⋊#64470, C2×C3×C23⋊#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 41);