Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| isoclinism | isoclinic class of D37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×#66524⋊C2 |
| derived, Sylow | C37 ⋊ C2×C3×C9 |
| Hall | C3×#66524 ⋊ C2 |
| Hall | D37 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D37⋊C3 |
| commutator, hypocenter | C37 | C2×C3×C9 |
| Frattini | C3 | C3×D37⋊C3 |
| Fitting, socle | C32×C37 | C2×C3 |
| prime radical | C32×D37 | C3 |
| cosocle | C3×C37 | C2×C32 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C32 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 999 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 12);