Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #67356⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#67356⋊C2 |
| unambiguous semidirect product | #67356⋊C22 |
| unambiguous semidirect product | #67361⋊C22 |
| unambiguous semidirect product | #67366⋊C22 |
| Fitting | C2×C7×C9 ⋊ C22×C3 |
| derived | C7×C9 ⋊ C23×C3 |
| Hall | #4427 ⋊ C23 |
| Sylow | C7 ⋊ C22×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #67356⋊C2 |
| commutator, cosocle, hypocenter | C7×C9 | C23×C3 |
| Frattini | C3 | C2×D3×AGL(1,𝔽7) |
| Fitting | C2×C7×C9 | C22×C3 |
| socle | C2×C3×C7 | C2×C3×D3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C2 | |
202 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 126 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | #72230027, C2×AGL(1,𝔽7)×AGL(1,ℤ/9), D3×#67356⋊C2, … |
| maximal normal subgroup of | C2×AGL(1,𝔽7)×AGL(1,ℤ/9), C22×#67356⋊C2 |
| maximal quotient of | #72230027, D3×#67356⋊C2, C22×#67356⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 465);