Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C3⋊#92259 |
| Fitting, Sylow | C3×#6891 ⋊ C2 |
833 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 833 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|b^3=f,d^a=d^2,e^a=e^2,g^a=g^2,c^b=cf,d^b=dg93 conjugacy classes — view the full character table.
| maximal subgroup of | #72221871, #72222316, #72243411, … |
| maximal normal subgroup of | #72221871, #72243419, 3−1+2×C3⋊((C3⋊D3)⋊C3), … |
| maximal quotient of | #72221835, #72222306, #72243411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1474);