Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #10624508 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C33 |
| direct product | C2×#10624508 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #6866 |
| commutator | C33 | C2×C3×C9 |
| Frattini, cosocle | C34 | C2×C32 |
| prime radical | C2×C32×H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C33 ◁ C2×C34 ◁ G | |
350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 54 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 68);