Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13090446 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | H(3,𝔽3)⋊C27 ⋊ C2 |
| derived | C32×C27 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C27 | C2×C3 |
| Frattini | C32×C9 | C3×D3 |
| Fitting | H(3,𝔽3)⋊C27 | C2 |
| socle | C32 | #4169 |
| LCS | G ▷ C32×C27 | |
| UCS | C1 | |
117 conjugacy classes of subgroups.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
2,3^6|b^3=e,e^3=g,b^a=b^2c^2de^2fg^2,c^a=cd^2f,d^a=d^2,e^a=e^2g^2,f^a=f^2,g^a=g^2,c^b=cd,d^b=df,d^c=df81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 520);