Finite Group DatabasebetaFinite Group Databasebeta| order | 7946 |
| automorphism | Aut(G) order 15129184 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3973 |
| unambiguous semidirect product | C29⋊D137 |
| unambiguous semidirect product | C137⋊D29 |
| Fitting, socle, derived, Hall | C29×C137 ⋊ C2 |
| Sylow | C137 ⋊ D29 |
| Sylow | C29 ⋊ D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C137 | C2 |
| LCS | G ▷ C29×C137 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,29,137|b^a=b^28,c^a=c^1361988 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30629611, #30629612, D29×D137, … |
| maximal normal subgroup of | #30629611, #30629612, D29×D137, … |
| maximal quotient of | Dic3973, C2×D3973, C3×D3973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7946, 3);