Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624555 ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C2×C9 |
386 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 40 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|b^3=g,c^3=g,b^a=b^2c^2e^2g^2,d^a=d^2,e^a=e^2,c^b=ce,d^b=df117 conjugacy classes — view the full character table.
| maximal subgroup of | #72221835, #72221854, C2×#13090642 |
| maximal normal subgroup of | #72221835, #72221854, C2×#13090642 |
| maximal quotient of | #72221829, C2×#13090642 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 716);