Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624752 ⋊ C2 |
200 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=g,d^3=g,b^a=bcd^2e^2fg^2,c^a=d,d^a=c,e^a=fg^2,f^a=eg,c^b=ce,d^b=df,e^b=eg,f^c=fg,e^d=eg54 conjugacy classes — view the full character table.
| maximal subgroup of | #72243618, #72243619, C3×#13091125, … |
| maximal normal subgroup of | #72243618, #72243619, C3×#13091125, … |
| maximal quotient of | C3×#13091125 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1199);