Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #4207 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32 |
| direct product | C9×#4207 |
| Fitting, Sylow | C9×#737 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #4207 |
| commutator, hypocenter | C3×C9 | C2×C3×C9 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | C9×#737 | C2 |
| prime radical | C3×#4207 | C3 |
| cosocle | C32×C9 | C2×C32 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C9 | |
356 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | #72243277, D9×#4207 |
| maximal normal subgroup of | #72243277, D9×#4207 |
| maximal quotient of | C9×#92299, C9×#92303 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1447);