Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C2×C9×C37⋊C3 |
| Fitting | C2×C9×C37 ⋊ C3 |
| derived, Sylow | C37 ⋊ C2×C3×C9 |
| Hall | C2×C37 ⋊ C3×C9 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 666 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9×#66526, C2×C9×D37⋊C3, C4×C9×C37⋊C3, … |
| maximal normal subgroup of | C2×C9×#66526, C2×C9×D37⋊C3, C4×C9×C37⋊C3, … |
| maximal quotient of | C4×C9×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 25);