Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13091513 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | H(3,𝔽3)×3−1+2 ⋊ C2 |
| derived | C32×C9 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | H(3,𝔽3)×3−1+2 | C2 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 | |
497 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 497 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|c^3=f,b^a=b^2d^2eg^2,c^a=c^2f^2,f^a=f^2,g^a=g^2,c^b=cf,d^b=dg,e^c=ef74 conjugacy classes — view the full character table.
| maximal subgroup of | #72243233, (C3⋊D3)⋊C3×AGL(1,ℤ/9), #72243468, … |
| maximal normal subgroup of | (C3⋊D3)⋊C3×AGL(1,ℤ/9), #72243480, #72243481, … |
| maximal quotient of | #72243231, #72243466, #72243468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1587);