Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of #3866⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#3866⋊C3 |
| unambiguous semidirect product | #3866⋊(C2×C3) |
| unambiguous semidirect product | (D37⋊C3)⋊C4 |
| unambiguous semidirect product | (C2×#3866)⋊C3 |
| Fitting, socle | C2×C37 ⋊ C3×C4 |
| derived, Sylow | C37 ⋊ C2×C3×C4 |
| Hall | C2×#3866 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #3866⋊C3 |
| commutator, hypocenter | C37 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37 | C3×C4 |
| prime radical | C2×D37⋊C3 | C2 |
| cosocle | D37 | C22×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 74 |
30 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#3866⋊C3, C4⋊(#3866⋊C3), (C22⋊#3866)⋊C3, … |
| maximal normal subgroup of | C4×#3866⋊C3, C4⋊(#3866⋊C3), (C22⋊#3866)⋊C3, … |
| maximal quotient of | (D37⋊C3)⋊C8, #10596953⋊C3, C4×#3866⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 45);