Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊#63120) |
| Fitting, socle, derived, Hall | C5×C112×C13 ⋊ C4 |
| Hall | C112×C13 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ Dic13 |
| Sylow | C112 ⋊ #63120 |
| Hall | C5×C13 ⋊ C11⋊Dic11 |
| Sylow | C13 ⋊ C11⋊(C11⋊AGL(1,𝔽5)) |
| Sylow | C5 ⋊ C11⋊Dic143 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C112×C13 | C4 |
| prime radical, cosocle | D5×C112×C13 | C2 |
| LCS | G ▷ C5×C112×C13 | |
| UCS | C1 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
Polycyclic presentation:
2^2,5,11^2,13|a^2=b,c^a=c^2,d^a=d^10,e^a=e^10,f^a=f^12,c^b=c^43149 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 195);