Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #92160 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#92160 |
| Fitting, Sylow | C3×#6856 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #4179 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C32 |
| Frattini | C33 | C32×D3 |
| Fitting | C3×#6856 | C2 |
| socle | C33 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C32 | |
245 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 245 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 758);