Finite Group DatabasebetaFinite Group Databasebeta| order | 12772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D31×D103 |
| unambiguous semidirect product | (D31×C103)⋊C2 |
| unambiguous semidirect product | (C31×D103)⋊C2 |
| unambiguous semidirect product | D3193⋊C2 |
| Fitting, socle, derived, Hall | C31×C103 ⋊ C22 |
| Sylow | C103 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C103 | C22 |
| LCS | G ▷ C31×C103 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
901 conjugacy classes — view the full character table.
| maximal subgroup of | #34062513⋊C2, #34062514⋊C2, D31⋊C3×D103, … |
| maximal normal subgroup of | #34062513⋊C2, #34062514⋊C2, D31⋊C3×D103, … |
| maximal quotient of | C3×D31×D103, D93×D103, D31×D309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12772, 6);