Finite Group DatabasebetaFinite Group Databasebeta| order | 9890 |
| isoclinism | isoclinic class of D115 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D115 |
| unambiguous semidirect product | C5⋊(C43×D23) |
| unambiguous semidirect product | C23⋊(D5×C43) |
| Fitting, socle, Hall | C5×C23×C43 ⋊ C2 |
| derived, Hall | C5×C23 ⋊ C2×C43 |
| Hall | C23×C43 ⋊ D5 |
| Hall | C5×C43 ⋊ D23 |
| Sylow | C23 ⋊ D5×C43 |
| Sylow | C5 ⋊ C43×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D115 |
| commutator, cosocle, hypocenter | C5×C23 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C43 | C2 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
2537 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D115, D5×C43×D23, D115⋊D43, … |
| maximal normal subgroup of | D43×D115, D5×C43×D23, D115⋊D43, … |
| maximal quotient of | C43×Dic115, C2×C43×D115, C3×C43×D115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9890, 7);