Finite Group DatabasebetaFinite Group Databasebeta| order | 31410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C5×C349 ⋊ C2×C3 |
| derived, Sylow | C349 ⋊ C2×C32×C5 |
| Hall | C3×C5×C349⋊C3 ⋊ C2 |
| Hall | C5×D349 ⋊ C32 |
| Hall | C3×C349⋊C3 ⋊ C2×C5 |
| Hall | C5×C349 ⋊ C2×C32 |
| Hall | D349 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D349⋊C3 |
| commutator, cosocle, hypocenter | C349 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C349 | C2×C3 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C3×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5235 |
960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31410, 14);