Finite Group DatabasebetaFinite Group Databasebeta| order | 12346 |
| automorphism | Aut(G) order 38099756 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D6173 |
| unambiguous semidirect product | C6173⋊C2 |
| Fitting, socle, derived, Sylow | C6173 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6173 | C2 |
| LCS | G ▷ C6173 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,6173|b^a=b^61723088 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37590742, C2×D6173, C3×D6173, … |
| maximal normal subgroup of | #37590742, C2×D6173, C3×D6173 |
| maximal quotient of | Dic6173, C2×D6173, C3×D6173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12346, 1);