Finite Group DatabasebetaFinite Group Databasebeta| order | 12492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic1041 |
| unambiguous semidirect product | C3⋊(C3×Dic347) |
| unambiguous semidirect product | C347⋊(C3×Dic3) |
| derived | C3×C347 ⋊ C3×C4 |
| Hall | C32×C347 ⋊ C4 |
| Sylow | C347 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ Dic347 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1041 |
| commutator, hypocenter | C3×C347 | C3×C4 |
| Frattini | C2 | C3×D1041 |
| Fitting, socle, prime radical | C2×C32×C347 | C2 |
| cosocle | C2×C3×C347 | C2×C3 |
| LCS | G ▷ C3×C347 | |
| UCS | C1 ◁ C2×C3 | |
28 conjugacy classes of subgroups.
3132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12492, 14);