Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624742 ⋊ C2 |
419 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 419 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|b^3=g^2,b^a=bce^2g,c^a=c^2g^2,e^a=e^2g^2,c^b=ce,d^b=df,e^b=eg,e^c=eg86 conjugacy classes — view the full character table.
| maximal subgroup of | #72277559, #72277654, #72277672 |
| maximal quotient of | #72277527, #72277528, #72277672 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1160);