Finite Group DatabasebetaFinite Group Databasebeta| order | 31380 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C523⋊C3)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C523⋊AGL(1,𝔽5))⋊C3 |
| Fitting, socle, derived, Hall | C5×C523 ⋊ C3×C4 |
| Hall | C523⋊AGL(1,𝔽5) ⋊ C3 |
| Hall | C5×C523⋊C3 ⋊ C4 |
| Hall | C523⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C523 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ (C523⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C523 | C3×C4 |
| prime radical | D5×C523⋊C3 | C2 |
| cosocle | D5×C523 | C2×C3 |
| LCS | G ▷ C5×C523 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2615 |
Polycyclic presentation:
2,3,2,5,523|a^2=c,d^a=d^2,e^a=e^522,e^b=e^60,d^c=d^4363 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31380, 14);