Finite Group DatabasebetaFinite Group Databasebeta| order | 8060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊#63122 |
| Fitting, socle, derived, Hall | C5×C13×C31 ⋊ C4 |
| Hall | C13×C31 ⋊ AGL(1,𝔽5) |
| Hall | C5×C31 ⋊ #261 |
| Hall | C5×C13 ⋊ Dic31 |
| Sylow | C31 ⋊ #63122 |
| Sylow | C13 ⋊ C31⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C31⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C31 | C4 |
| LCS | G ▷ C5×C13×C31 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,13,31|a^2=b,c^a=c^2,d^a=d^5,e^a=e^30,c^b=c^4,d^b=d^12530 conjugacy classes — view the full character table.
| maximal subgroup of | #37563834, #37563835, #37563838, … |
| maximal normal subgroup of | #37563834, #37563835, #37563838, … |
| maximal quotient of | C3×C31⋊#63122, C3⋊(C31⋊#63122) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8060, 27);