Finite Group DatabasebetaFinite Group Databasebeta| order | 930 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D31 |
| Fitting, socle, Hall | C3×C5×C31 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C3×C5 |
| Hall | C5×C31 ⋊ C2×C3 |
| Hall | C3×C31 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D31 |
| commutator, cosocle, hypocenter | C31 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C31 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 465 |
255 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×D31, C5×D3×D31, D15×D31, … |
| maximal normal subgroup of | C3×D5×D31, C5×D3×D31, D15×D31, … |
| maximal quotient of | C3×C5×Dic31, C2×C3×C5×D31, C5×C9×D31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(930, 11);