Finite Group DatabasebetaFinite Group Databasebeta| order | 30411 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C109 · Schur multiplier (H2) = C3 |
| direct product | C3×C31⋊C3×C109 |
| unambiguous semidirect product | C31⋊(C32×C109) |
| unambiguous semidirect product | (C3×C31)⋊(C3×C109) |
| Fitting, socle | C3×C31×C109 ⋊ C3 |
| derived, Sylow | C31 ⋊ C32×C109 |
| Hall | C31×C109 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C109 | C31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C32×C109 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C109 | C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C109 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10137 |
4251 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30411, 12);