Finite Group DatabasebetaFinite Group Databasebeta| order | 7906 |
| automorphism | Aut(G) order 15132084 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3953 |
| unambiguous semidirect product | C59⋊D67 |
| unambiguous semidirect product | C67⋊D59 |
| Fitting, socle, derived, Hall | C59×C67 ⋊ C2 |
| Sylow | C67 ⋊ D59 |
| Sylow | C59 ⋊ D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C59×C67 | C2 |
| LCS | G ▷ C59×C67 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,59,67|b^a=b^58,c^a=c^661978 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×D67, C2×D3953, C3×D3953, … |
| maximal normal subgroup of | D59×D67, C2×D3953, C3×D3953, … |
| maximal quotient of | Dic3953, C2×D3953, C3×D3953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7906, 3);