Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of C3⋊#3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×C3⋊#3874 |
| unambiguous semidirect product | C3⋊(C23×#3874) |
| Fitting, socle | C3×C52×C23 ⋊ D3 |
| derived, Hall | C3×C52⋊C3 ⋊ C2×C23 |
| Hall | C3×C23×C52⋊C3 ⋊ C2 |
| Hall | C52×C23 ⋊ C3⋊D3 |
| Sylow | C52 ⋊ C3⋊D3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊#3874 |
| commutator, cosocle, hypocenter | C3×C52⋊C3 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C23 | D3 |
| LCS | G ▷ C3×C52⋊C3 | |
| UCS | C1 ◁ C23 | |
64 conjugacy classes of subgroups.
552 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#3874⋊D3, #35208101, C23×((C5⋊D5)⋊C3)⋊D3, … |
| maximal normal subgroup of | C23×#3874⋊D3, #35208101, C23×((C5⋊D5)⋊C3)⋊D3, … |
| maximal quotient of | C23×C3⋊#64470, C2×C23×C3⋊#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 45);