Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624884 ⋊ C2 |
272 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 51 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=g,c^3=f,c^a=c^2f^2,e^a=e^2,f^a=f^2,c^b=cf,d^b=dg,e^b=ef,d^c=df69 conjugacy classes — view the full character table.
| maximal subgroup of | #72243277, #72243533, #72277494, … |
| maximal normal subgroup of | #72243277, #72243533, #72277553 |
| maximal quotient of | #72243272, #72243889 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1553);