Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of D37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×D37⋊C3 |
| unambiguous semidirect product | D37⋊(C22×C3) |
| unambiguous semidirect product | (C37⋊C3)⋊C23 |
| unambiguous semidirect product | (C2×C37⋊C3)⋊C22 |
| Fitting, socle | C22×C37 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C23×C3 |
| Hall | C22×D37 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C37 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C22 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 148 |
48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 49);