Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C3 |
| direct product | C5×C23×C3⋊D15 |
| unambiguous semidirect product | C3⋊(C5×C23×D15) |
| unambiguous semidirect product | C5⋊(C5×C3⋊D3×C23) |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C2 |
| derived | C32×C5 ⋊ C2×C5×C23 |
| Hall | C52×C23 ⋊ C3⋊D3 |
| Hall | C32×C52 ⋊ C2×C23 |
| Hall | C32×C23 ⋊ C5×D5 |
| Sylow | C52 ⋊ C3⋊D3×C23 |
| Sylow | C32 ⋊ C5×D5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C23 | C3⋊D15 |
| commutator, cosocle, hypocenter | C32×C5 | C2×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C23 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C5×C23 | |
120 conjugacy classes of subgroups.
2760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C23×#4380, C5×C23⋊#4380, C23×#11744709, … |
| maximal normal subgroup of | C5×C23×#4380, C5×C23⋊#4380, C23×#11744709, … |
| maximal quotient of | C5×C23×C3⋊Dic15, C2×C5×C23×C3⋊D15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 55);