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 | C2×Dic37⋊C3 |
| unambiguous semidirect product | (C2×Dic37)⋊C3 |
| derived, Sylow | C37 ⋊ C2×C3×C4 |
| Hall | C2×Dic37 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D37⋊C3 |
| commutator, hypocenter | C37 | C2×C3×C4 |
| Frattini | C2 | C2×D37⋊C3 |
| Fitting, socle | C22×C37 | C2×C3 |
| prime radical | C22×C37⋊C3 | C2 |
| cosocle | C2×C37 | C22×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Dic37⋊C3, #10596936⋊C3, C4⋊(Dic37⋊C3), … |
| maximal normal subgroup of | C4×Dic37⋊C3, #10596936⋊C3, C4⋊(Dic37⋊C3), … |
| maximal quotient of | C2×#64436⋊C3, #10596934⋊C3, C4×Dic37⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 11);