Finite Group DatabasebetaFinite Group Databasebeta| order | 31140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C173 · Schur multiplier (H2) = C3 |
| direct product | C173×C3⋊ΓL(1,𝔽16) |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽16)×C173) |
| Fitting, socle, Hall | C32×C5×C173 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C4×C173 |
| Hall | C32×C173 ⋊ AGL(1,𝔽5) |
| Hall | C5×C173 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ AGL(1,𝔽5)×C173 |
| Sylow | C5 ⋊ C3⋊Dic3×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C173 | C3⋊ΓL(1,𝔽16) |
| commutator, hypocenter | C32×C5 | C4×C173 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C173 | C4 |
| prime radical | C32×D5×C173 | C2 |
| cosocle | C32×D5 | C2×C173 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C173 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7785 |
3633 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31140, 91);