Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | H(3,𝔽9) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92391 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | H(3,𝔽9) | C2 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
479 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|c^a=b^2c^2g,d^a=bc^2dg^2,e^a=c^2d^2e^2f^2,f^a=f^2,g^a=f^2g,c^b=cf,d^b=dg,e^b=efg,d^c=df^2g,e^c=ef61 conjugacy classes — view the full character table.
| maximal subgroup of | #72277600, #72277623 |
| maximal normal subgroup of | #72277600 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1611);