Finite Group DatabasebetaFinite Group Databasebeta| order | 7442 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C61 |
| unambiguous semidirect product | C61⋊D61 |
| Fitting, socle, derived, Sylow | C612 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C612 | C2 |
| LCS | G ▷ C612 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2,61^2|b^a=b^60,c^a=c^601862 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D612, #28415646, #28415647, … |
| maximal normal subgroup of | D612, #28415646, #28415647, … |
| maximal quotient of | #28415641, C2×C61⋊D61, C3×C61⋊D61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7442, 4);