Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | #10624748 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3 | #92301 |
| commutator, cosocle, hypocenter | H(5,𝔽3) | C2×C3 |
| Frattini | C33 | C3×C3⋊D3 |
| Fitting | #10624748 | C2 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C3 | |
330 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|b^3=g,b^a=bde^2f,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^2g^2,c^b=ce,d^b=df,e^b=eg,f^c=fg,e^d=eg42 conjugacy classes — view the full character table.
| maximal subgroup of | #72277519 |
| maximal normal subgroup of | #72277519 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1185);