Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C2×#10624502 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C27 | H(3,𝔽3) |
| commutator | C32 | C2×C3×C27 |
| Frattini, cosocle | C3×C27 | C2×C32 |
| socle | C2×C3 | C32⋊C27 |
| prime radical | C2×C33 | C27 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C27 ◁ C2×C3×C27 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 162 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 62);