Finite Group DatabasebetaFinite Group Databasebeta| order | 10707 |
| isoclinism | isoclinic class of C43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×C43⋊C3 |
| unambiguous semidirect product | C43⋊(C3×C83) |
| unambiguous semidirect product | (C43×C83)⋊C3 |
| Fitting, socle, Hall | C43×C83 ⋊ C3 |
| derived, Sylow | C43 ⋊ C3×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | C43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C3×C83 |
| Frattini | C1 | G |
| Fitting, socle | C43×C83 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C83 | |
8 conjugacy classes of subgroups.
1411 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C83×C43⋊C3, C43⋊C3×D83, C83×D43⋊C3, … |
| maximal normal subgroup of | C2×C83×C43⋊C3, C43⋊C3×D83, C83×D43⋊C3, … |
| maximal quotient of | C2×C83×C43⋊C3, C83×C43⋊C9, C3×C83×C43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10707, 1);