Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624558 ⋊ C2 |
245 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 245 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=fg,b^a=bc,c^a=c^2f^2g^2,e^a=e^2,g^a=fg^2,c^b=ce,d^b=df93 conjugacy classes — view the full character table.
| maximal subgroup of | #72221846, #72243522, #72243527, … |
| maximal normal subgroup of | #72221846, #72243529, C2×#13090650 |
| maximal quotient of | #72221844, C2×#13090650 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 724);