Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13091666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | #10624936 ⋊ C2 |
| derived | C32×C9 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C9 | C2×C32 |
| Frattini | C32 | C32×C3⋊D3 |
| Fitting | #10624936 | C2 |
| socle | C3 | C3×C3⋊((C3⋊D3)⋊C3) |
| LCS | G ▷ C32×C9 | |
| UCS | C1 | |
360 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 360 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.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|c^3=g^2,d^3=g,c^a=c^2g,d^a=d^2g^2,f^a=f^2,g^a=g^2,c^b=cf,f^b=fg,e^d=eg66 conjugacy classes — view the full character table.
| maximal subgroup of | #72243686, #72243852 |
| maximal normal subgroup of | #72243686, #72243852 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1740);