Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10624828 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C3 |
| direct product | C2×#10624828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #6895 |
| commutator, Frattini, cosocle | C3×C9 | C2×C33 |
| prime radical | C2×C33 | 3−1+2 |
| LCS | G ▷ C3×C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C3×C9 ◁ G | |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 54 |
114 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×#10624828⋊C2 |
| maximal subgroup of | C2×#14546414, C2×#14554636, C2×#10624828⋊C2 |
| maximal normal subgroup of | C2×#14546414, C2×#14554636, C2×#10624828⋊C2 |
| maximal quotient of | C2×#14550487 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 388);