Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C42×C3⋊D21 |
| Fitting | C32×C42×C7 ⋊ C2 |
| derived, Hall | C32×C7 ⋊ C2×C42 |
| Sylow | C32 ⋊ C42×D7 |
| Sylow | C7 ⋊ C42×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | C3⋊D21 |
| commutator, hypocenter | C32×C7 | C2×C42 |
| Frattini | C22 | C22×C3⋊D21 |
| Fitting | C32×C42×C7 | C2 |
| socle, cosocle | C22×C32×C7 | C23 |
| prime radical | C22×C3⋊D21 | C22 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C42 | |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C42×D7×C3⋊D3, #127×C3⋊D21, #72246389, … |
| maximal normal subgroup of | C42×D7×C3⋊D3, #127×C3⋊D21, #72246389, … |
Past the SmallGroups library coverage — no SmallGroups id.