Finite Group DatabasebetaFinite Group Databasebeta| order | 6946 |
| automorphism | Aut(G) order 11460900 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3473 |
| unambiguous semidirect product | C23⋊D151 |
| unambiguous semidirect product | C151⋊D23 |
| Fitting, socle, derived, Hall | C23×C151 ⋊ C2 |
| Sylow | C151 ⋊ D23 |
| Sylow | C23 ⋊ D151 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C151 | C2 |
| LCS | G ▷ C23×C151 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,23,151|b^a=b^22,c^a=c^1501738 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D151, C2×D3473, C3×D3473, … |
| maximal normal subgroup of | D23×D151, C2×D3473, C3×D3473, … |
| maximal quotient of | Dic3473, C2×D3473, C3×D3473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6946, 3);