Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | #10624474 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3 | #92198 |
| commutator, Fitting, cosocle, hypocenter | #10624474 | C2 |
| Frattini | C34 | C3⋊D3 |
| LCS | G ▷ #10624474 | |
| UCS | C1 ◁ C3 | |
214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2,3^6|b^a=b^2,c^a=c^2,d^a=de^2f^2g,e^a=e^2g,f^a=f^2g,c^b=cd,d^b=de,f^b=fg,d^c=df,e^c=eg34 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 575);