Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6875 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C32 |
| direct product | C2×#10624709 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C9 | C9⋊C9 |
| commutator | C9 | C2×C32×C9 |
| Frattini, cosocle | C3×C9 | C2×C33 |
| socle | C2×C3 | C3×C9⋊C9 |
| prime radical | C2×C33 | 3−1+2 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C9 ◁ C2×C32×C9 ◁ G | |
198 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 162 |
210 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×#10624709⋊C2 |
| maximal subgroup of | C2×#14554150, C2×#14554636, C2×#14550738, … |
| maximal normal subgroup of | C2×#14554150, C2×#14554636, C2×#14550738, … |
| maximal quotient of | C2×C9×#6875 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 269);