Finite Group DatabasebetaFinite Group Databasebeta| order | 7006 |
| automorphism | Aut(G) order 11770080 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3503 |
| unambiguous semidirect product | C31⋊D113 |
| unambiguous semidirect product | C113⋊D31 |
| Fitting, socle, derived, Hall | C31×C113 ⋊ C2 |
| Sylow | C113 ⋊ D31 |
| Sylow | C31 ⋊ D113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C113 | C2 |
| LCS | G ▷ C31×C113 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,31,113|b^a=b^30,c^a=c^1121753 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D113, C2×D3503, C3×D3503, … |
| maximal normal subgroup of | D31×D113, C2×D3503, C3×D3503, … |
| maximal quotient of | Dic3503, C2×D3503, C3×D3503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7006, 3);