Finite Group DatabasebetaFinite Group Databasebeta| order | 12854 |
| automorphism | Aut(G) order 41299902 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D6427 |
| unambiguous semidirect product | C6427⋊C2 |
| Fitting, socle, derived, Sylow | C6427 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6427 | C2 |
| LCS | G ▷ C6427 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,6427|b^a=b^64263215 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D6427, D6427⋊C3, C3×D6427, … |
| maximal normal subgroup of | C2×D6427, D6427⋊C3, C3×D6427 |
| maximal quotient of | Dic6427, C2×D6427, C3×D6427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12854, 1);