Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33×C9 · Schur multiplier (H2) = C35 |
| direct product | C2×#10624862 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C34 |
| commutator | C3 | C2×C33×C9 |
| Frattini, cosocle | C32 | C2×C34 |
| prime radical | C2×C32×H(3,𝔽3) | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
1178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
498 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 422);