Finite Group DatabasebetaFinite Group Databasebeta| order | 30042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C1669⋊C3 |
| unambiguous semidirect product | (C2×C1669)⋊C32 |
| unambiguous semidirect product | (C2×C3×C1669)⋊C3 |
| Fitting, socle | C2×C3×C1669 ⋊ C3 |
| derived, Sylow | C1669 ⋊ C2×C32 |
| Hall | C2×C1669 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C1669⋊C3 |
| commutator, cosocle, hypocenter | C1669 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C1669 | C3 |
| LCS | G ▷ C1669 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10014 |
3354 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30042, 11);