Finite Group DatabasebetaFinite Group Databasebeta| order | 31902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C409 · Schur multiplier (H2) = C1 |
| direct product | D13⋊C3×C409 |
| unambiguous semidirect product | D13⋊(C3×C409) |
| unambiguous semidirect product | (C13⋊C3)⋊(C2×C409) |
| Fitting, socle, Hall | C13×C409 ⋊ C2×C3 |
| derived, Sylow | C13 ⋊ C2×C3×C409 |
| Hall | C13⋊C3×C409 ⋊ C2 |
| Hall | D13×C409 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×C409 |
| Hall | D13 ⋊ C3×C409 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C409 | D13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C2×C3×C409 |
| Frattini | C1 | G |
| Fitting, socle | C13×C409 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C409 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5317 |
3272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31902, 18);