Finite Group DatabasebetaFinite Group Databasebeta| order | 7998 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1 |
| direct product | C3×C43×D31 |
| Fitting, socle, Hall | C3×C31×C43 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C3×C43 |
| Hall | C31×C43 ⋊ C2×C3 |
| Hall | C3×C31 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | D31 |
| commutator, hypocenter | C31 | C2×C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C43 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C43 | |
16 conjugacy classes of subgroups.
2193 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D31×D43, D3×C43×D31, D31×D129, … |
| maximal normal subgroup of | C3×D31×D43, D3×C43×D31, D31×D129, … |
| maximal quotient of | C3×C43×Dic31, C2×C3×C43×D31, C9×C43×D31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7998, 7);