Finite Group DatabasebetaFinite Group Databasebeta| order | 12442 |
| automorphism | Aut(G) order 38694620 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D6221 |
| unambiguous semidirect product | C6221⋊C2 |
| Fitting, socle, derived, Sylow | C6221 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6221 | C2 |
| LCS | G ▷ C6221 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,6221|b^a=b^62203112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #38733475, C2×D6221, C3×D6221, … |
| maximal normal subgroup of | #38733475, C2×D6221, C3×D6221 |
| maximal quotient of | Dic6221, C2×D6221, C3×D6221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12442, 1);