Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13090656 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3×C9 |
No aliases for this group.
| Fitting, Sylow | #10624560 ⋊ C2 |
| derived | C3×C92 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C92 | C2×C3 |
| Frattini, socle | C33 | C3×C3⋊D3 |
| Fitting | #10624560 | C2 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 | |
347 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=g,d^3=f,b^a=bc,c^a=c^2g^2,d^a=d^2f^2,e^a=e^2,f^a=f^2,g^a=g^2,c^b=ce,d^b=df81 conjugacy classes — view the full character table.
| maximal subgroup of | #72243205, #72243228, #72243231, … |
| maximal normal subgroup of | #72243231, #72243347 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 730);