Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C192 · Schur multiplier (H2) = C19 |
| direct product | C5×D3×C192 |
| unambiguous semidirect product | C3⋊(C2×C5×C192) |
| Fitting, socle, Hall | C3×C5×C192 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C5×C192 |
| Hall | C3×C192 ⋊ C2×C5 |
| Hall | C3×C5 ⋊ C2×C192 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C192 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C5×C192 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C192 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C5×C192 | |
176 conjugacy classes of subgroups.
5415 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×C19×D19, C5×D3×C19⋊D19, D3×D5×C192, … |
| maximal normal subgroup of | C5×D3×C19×D19, C5×D3×C19⋊D19, D3×D5×C192, … |
| maximal quotient of | C5×Dic3×C192, C2×C5×D3×C192, C5×D9×C192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 50);