Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C34 |
| unambiguous semidirect product | C3⋊((C3⋊D3)⋊H(3,𝔽3)) |
| Fitting, Sylow | C3×C32⋊H(3,𝔽3) ⋊ C2 |
1175 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 1175 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|c^a=c^2,d^a=de,e^a=e^2,f^a=f^2,c^b=cf,d^b=dg93 conjugacy classes — view the full character table.
| maximal subgroup of | #72214199, D3×(C3⋊D3)⋊H(3,𝔽3), #72214728, … |
| maximal normal subgroup of | #72214199, D3×(C3⋊D3)⋊H(3,𝔽3), #72214728, … |
| maximal quotient of | C3×C3⋊((C3⋊D3)⋊H(3,𝔽3)), #72277541, #72277663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1464);