Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#3866 |
| Fitting, socle | C2×C3×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C2×C3×C4 |
| Hall | C3×C37 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #3866 |
| commutator, hypocenter | C37 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C37 | C4 |
| prime radical | C2×C3×D37 | C2 |
| cosocle | D37 | C22×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 222 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#3866, (C2×D3)⋊#3866, Dic3⋊#3866, … |
| maximal normal subgroup of | Dic3×#3866, (C2×D3)⋊#3866, Dic3⋊#3866, … |
| maximal quotient of | C3×D37⋊C8, C3×#10596953, C3×C4×#3866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 52);