Finite Group DatabasebetaFinite Group Databasebeta| order | 10230 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×D55 |
| unambiguous semidirect product | C5⋊(D11×C31⋊C3) |
| unambiguous semidirect product | C11⋊(D5×C31⋊C3) |
| unambiguous semidirect product | (C31×D55)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C31 | C2×C3 |
| LCS | G ▷ C5×C11×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
377 conjugacy classes — view the full character table.
| maximal subgroup of | D55×D31⋊C3, D55⋊(D31⋊C3), D5×D11×C31⋊C3, … |
| maximal normal subgroup of | D55×D31⋊C3, D55⋊(D31⋊C3), D5×D11×C31⋊C3, … |
| maximal quotient of | C31⋊C3×Dic55, C2×C31⋊C3×D55, D55×C31⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10230, 77);