Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of D111 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic111 |
| unambiguous semidirect product | (C2×C3)⋊Dic37 |
| derived, Hall | C3×C37 ⋊ C2×C4 |
| Sylow | C37 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C2×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D111 |
| commutator, hypocenter | C3×C37 | C2×C4 |
| Frattini | C2 | C2×D111 |
| Fitting, socle, prime radical | C22×C3×C37 | C2 |
| cosocle | C2×C3×C37 | C22 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 888 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×Dic37, #13183837, (C2×D3)⋊Dic37, … |
| maximal normal subgroup of | Dic3×Dic37, #13183837, (C2×D3)⋊Dic37, … |
| maximal quotient of | C2×C3⋊#64436, #13183891, C4×Dic111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 40);