Finite Group DatabasebetaFinite Group Databasebeta| order | 7442 |
| automorphism | Aut(G) order 13618860 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3721 |
| unambiguous semidirect product | C3721⋊C2 |
| Fitting, derived, Sylow | C3721 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3721 | C2 |
| Frattini, socle | C61 | D61 |
| LCS | G ▷ C3721 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2,61^2|b^61=c,b^a=b^60c^60,c^a=c^601862 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28415637, C2×D3721, D3721⋊C3, … |
| maximal normal subgroup of | #28415637, C2×D3721, D3721⋊C3, … |
| maximal quotient of | Dic3721, C2×D3721, C3×D3721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7442, 1);