Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C11 |
| direct product | C13×C11⋊(C11⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C11⋊(C13×C11⋊AGL(1,𝔽5)) |
| Fitting, socle, Hall | C5×C112×C13 ⋊ C4 |
| derived, Hall | C5×C112 ⋊ C4×C13 |
| Hall | C112×C13 ⋊ AGL(1,𝔽5) |
| Sylow | C112 ⋊ C13×AGL(1,𝔽5) |
| Hall | C5×C13 ⋊ C11⋊Dic11 |
| Sylow | C5 ⋊ C13×C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C11⋊(C11⋊AGL(1,𝔽5)) |
| commutator, hypocenter | C5×C112 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112×C13 | C4 |
| prime radical | D5×C112×C13 | C2 |
| cosocle | D5×C112 | C2×C13 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C13 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
3185 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 192);