Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C3⋊#92262 |
| Fitting, Sylow | C3×C9⋊H(3,𝔽3) ⋊ C2 |
479 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 479 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) = 162 |
Polycyclic presentation:
2,3^6|c^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 | #72243418, 3−1+2×C3⋊((C3⋊D3)⋊C3), #72243893, … |
| maximal normal subgroup of | 3−1+2×C3⋊((C3⋊D3)⋊C3), D3×#92262, #72254060, … |
| maximal quotient of | #72243418, #72243893, #72243898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1482);