Finite Group DatabasebetaFinite Group Databasebeta| order | 702 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C3 |
| direct product | C13×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (C3⋊D3)⋊(C3×C13) |
| Fitting, Hall | C13×H(3,𝔽3) ⋊ C2 |
| derived | C32 ⋊ C2×C3×C13 |
| Sylow | H(3,𝔽3) ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | (C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | C32 | C2×C3×C13 |
| Frattini | C3 | C3×D3×C13 |
| Fitting | C13×H(3,𝔽3) | C2 |
| socle | C3×C13 | C3×D3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C13 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 117 |
130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(702, 34);