Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D7×(C2×D3)⋊Dic3 |
| Hall | C32×C7 ⋊ C2×C22⋊C4 |
| Sylow | C32 ⋊ D7×C22⋊C4 |
| Sylow | C7 ⋊ C2×(C2×D3)⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D7 |
| commutator | C2×C32×C7 | C22×C4 |
| Fitting, socle, cosocle | C22×C32×C7 | C23 |
| prime radical | C22×C3×D3×D7 | C2 |
| hypocenter | C32×C7 | C2×C22⋊C4 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C22 | |
582 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#63921, D7×#63977, D7×#63983 |
| maximal normal subgroup of | D7×#63921, D7×#63977, D7×#63983 |
| maximal quotient of | D7×#63568 |
Past the SmallGroups library coverage — no SmallGroups id.