Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #92258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | #10624555 ⋊ C2 |
| derived | C33 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92258 |
| commutator, hypocenter | C33 | C2×C3×C9 |
| Frattini, socle | C33 | C32×D3 |
| Fitting | #10624555 | C2 |
| prime radical | C3×C3⋊((C3⋊D3)⋊C3) | C3 |
| cosocle | C34 | C2×C32 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C3 | |
341 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 47 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=g,b^a=b^2c^2e^2f^2g^2,c^a=cf^2,e^a=e^2,f^a=f^2,c^b=ce,d^b=df117 conjugacy classes — view the full character table.
| maximal subgroup of | #72243409, #72243419, #72253781 |
| maximal normal subgroup of | #72243419, #72253781 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 717);