Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of D115 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×D115 |
| unambiguous semidirect product | C5⋊(C32×C5×D23) |
| unambiguous semidirect product | C23⋊(C32×C5×D5) |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C2 |
| derived | C5×C23 ⋊ C2×C32×C5 |
| Hall | C52×C23 ⋊ C2×C32 |
| Hall | C32×C52 ⋊ D23 |
| Hall | C32×C23 ⋊ C5×D5 |
| Sylow | C52 ⋊ C32×D23 |
| Sylow | C23 ⋊ C32×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | D115 |
| commutator, cosocle, hypocenter | C5×C23 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C23 | C2 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C32×C5 | |
120 conjugacy classes of subgroups.
2655 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C5×D5×D23, C32×D5×D115, C32×(C5⋊D5)⋊D23, … |
| maximal normal subgroup of | C32×C5×D5×D23, C32×D5×D115, C32×(C5⋊D5)⋊D23, … |
| maximal quotient of | C32×C5×Dic115, C2×C32×C5×D115 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 66);