Finite Group DatabasebetaFinite Group Databasebeta| order | 12492 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic347 |
| unambiguous semidirect product | C347⋊(C32×C4) |
| derived, Sylow | C347 ⋊ C32×C4 |
| Hall | C32×C347 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D347 |
| commutator, hypocenter | C347 | C32×C4 |
| Frattini | C2 | C32×D347 |
| Fitting, socle, prime radical | C2×C32×C347 | C2 |
| cosocle | C2×C347 | C2×C32 |
| LCS | G ▷ C347 | |
| UCS | C1 ◁ C2×C32 | |
36 conjugacy classes of subgroups.
3150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12492, 12);