Finite Group DatabasebetaFinite Group Databasebeta| order | 8868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×C739⋊C3 |
| unambiguous semidirect product | (C4×C739)⋊C3 |
| Fitting, Hall | C4×C739 ⋊ C3 |
| derived, Sylow | C739 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C739⋊C3 |
| commutator, hypocenter | C739 | C3×C4 |
| Frattini | C2 | C2×C739⋊C3 |
| Fitting | C4×C739 | C3 |
| socle | C2×C739 | C2×C3 |
| LCS | G ▷ C739 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
996 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#20268987, Dic3×C739⋊C3, C3×C4×C739⋊C3 |
| maximal normal subgroup of | C4×#20268987, C3×C4×C739⋊C3 |
| maximal quotient of | C4×#20268985, Dic3×C739⋊C3, C3×C4×C739⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8868, 3);