Finite Group DatabasebetaFinite Group Databasebeta| order | 12054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C7 |
| direct product | C3×C7⋊D287 |
| unambiguous semidirect product | C41⋊(C3×C7⋊D7) |
| Fitting, socle, Hall | C3×C72×C41 ⋊ C2 |
| derived, Hall | C72×C41 ⋊ C2×C3 |
| Hall | C3×C72 ⋊ D41 |
| Hall | C3×C41 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C3×D41 |
| Sylow | C41 ⋊ C3×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C7⋊D287 |
| commutator, cosocle, hypocenter | C72×C41 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C41 | C2 |
| LCS | G ▷ C72×C41 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
3018 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#22548818, C3×D7×D287, C3×D41×C7⋊D7, … |
| maximal normal subgroup of | C3×#22548818, C3×D7×D287, C3×D41×C7⋊D7, … |
| maximal quotient of | C3×C7⋊Dic287, C2×C3×C7⋊D287, C9×C7⋊D287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12054, 42);