Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | #10624463 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C9⋊D27 |
| commutator, Fitting, cosocle, hypocenter | #10624463 | C2 |
| Frattini | C32×C9 | C3⋊D3 |
| socle | C33 | C3⋊D9 |
| LCS | G ▷ #10624463 | |
| UCS | C1 ◁ C3 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 486 |
Polycyclic presentation:
2,3^6|b^3=e,c^3=f,e^3=g,b^a=b^2e^2g^2,c^a=c^2f^2,e^a=e^2g^2,f^a=f^2,g^a=g^2,c^b=cd153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 556);