Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D7⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D7⋊((C3⋊Dic3)⋊C3) |
| unambiguous semidirect product | (D7⋊H(3,𝔽3))⋊C4 |
| derived | C32×C7 ⋊ C2×C3×C4 |
| Hall | C7⋊H(3,𝔽3) ⋊ C2×C4 |
| Sylow | C7 ⋊ C2×(C3⋊Dic3)⋊C3 |
132 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 252 |
Polycyclic presentation:
2^2,3,2,3^2,7|b^2=d,g^a=g^6,e^b=e^2,f^b=f^2,e^c=ef,g^c=g^252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 129);