Finite Group DatabasebetaFinite Group Databasebeta| order | 930 |
| isoclinism | isoclinic class of C5⋊(D31⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D31⋊C3) |
| unambiguous semidirect product | (C31⋊C3)⋊D5 |
| unambiguous semidirect product | D155⋊C3 |
| Fitting, socle, derived, Hall | C5×C31 ⋊ C2×C3 |
| Hall | C5×C31⋊C3 ⋊ C2 |
| Hall | D155 ⋊ C3 |
| Hall | C31⋊C3 ⋊ D5 |
| Sylow | C31 ⋊ C3×D5 |
| Sylow | C5 ⋊ D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C31 | C2×C3 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 155 |
Polycyclic presentation:
2,3,5,31|c^a=c^4,d^a=d^30,d^b=d^2537 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D31⋊C3, C2×C5⋊(D31⋊C3), C3×C5⋊(D31⋊C3), … |
| maximal normal subgroup of | D5×D31⋊C3, C2×C5⋊(D31⋊C3), C3×C5⋊(D31⋊C3), … |
| maximal quotient of | (C31⋊C3)⋊Dic5, C2×C5⋊(D31⋊C3), C5⋊(D31⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(930, 8);