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,𝔽3)2 ⋊ 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,𝔽3)2 | C2 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
671 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18 |
Polycyclic presentation:
2,3^6|b^a=cd^2ef,c^a=bd^2eg^2,d^a=e,e^a=d,f^a=g,g^a=f,c^b=cf,d^b=dg,e^c=ef77 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, 1572);