Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of (#6880⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, Sylow | #10624852 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #733 | C2×C32 |
| Frattini | C3×C9 | C32×D3 |
| Fitting | #10624852 | C2 |
| socle | C3 | #92285 |
| LCS | G ▷ #733 | |
| UCS | C1 | |
101 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=f^2,e^3=g^2,b^a=b^2dg^2,e^a=e^2g,g^a=g^2,c^b=ce,e^b=ef,f^b=fg,d^c=df,e^d=eg^237 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(#6880⋊C2)⋊C3, #72222307, #72222314 |
| maximal normal subgroup of | C3×(#6880⋊C2)⋊C3 |
| maximal quotient of | #72222294, C3×(#6880⋊C2)⋊C3, #72222314 |
| automorphism group of | #733⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1396);