Finite Group DatabasebetaFinite Group Databasebeta| order | 12054 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C41×D49 |
| Fitting, Hall | C3×C41×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C3×C41 |
| Hall | C41×C49 ⋊ C2×C3 |
| Hall | C3×C49 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | D49 |
| commutator, cosocle, hypocenter | C49 | C2×C3×C41 |
| Frattini | C7 | C3×D7×C41 |
| Fitting | C3×C41×C49 | C2 |
| socle | C3×C7×C41 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C3×C41 | |
24 conjugacy classes of subgroups.
3198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D41×D49, D3×C41×D49, D49×D123, … |
| maximal normal subgroup of | C3×D41×D49, D3×C41×D49, D49×D123, … |
| maximal quotient of | C3×C41×Dic49, C2×C3×C41×D49, C9×C41×D49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12054, 7);