Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #10624535 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3 | #92191 |
| commutator, cosocle, hypocenter | #6879 | C2×C3 |
| Frattini | C92 | C3×D3 |
| Fitting | #10624535 | C2 |
| LCS | G ▷ #6879 | |
| UCS | C1 ◁ C3 | |
43 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|c^3=e^2f,d^3=f^2g,e^3=g^2,b^a=b^2,d^a=d^2e,e^a=ef,f^a=f^2,c^b=cd,d^b=de,e^b=ef,f^b=fg85 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 659);