Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of D37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D37⋊C3 |
| unambiguous semidirect product | (C4×D37)⋊C3 |
| Fitting | C4×C37 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C2×C3×C4 |
| Hall | C4×D37 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D37⋊C3 |
| commutator, hypocenter | C37 | C2×C3×C4 |
| Frattini | C2 | C2×D37⋊C3 |
| Fitting | C4×C37 | C2×C3 |
| socle, cosocle | C2×C37 | C22×C3 |
| prime radical | C2×D37⋊C3 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C4 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 148 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D37⋊C3, #10596929⋊C3, (D37⋊C3)⋊C8, … |
| maximal normal subgroup of | C8×D37⋊C3, #10596929⋊C3, (D37⋊C3)⋊C8, … |
| maximal quotient of | C8×D37⋊C3, #10596929⋊C3, C4×Dic37⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 9);