Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C81 · Schur multiplier (H2) = C32 |
| direct product | C2×C32⋊C81 |
| unambiguous semidirect product | (C2×C32)⋊C81 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C27 | C32 |
| commutator | C3 | C2×C3×C81 |
| Frattini, cosocle | C3×C27 | C2×C32 |
| socle | C2×C32 | C3×C27 |
| prime radical | C2×C33 | C27 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C27 ◁ G | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 486 |
594 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 61);