Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624732 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C32 | C3⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C32⋊H(3,𝔽3) | C2×C3 |
| Frattini | C33 | C3×C3⋊D3 |
| Fitting | #10624732 | C2 |
| LCS | G ▷ C32⋊H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
317 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 317 conjugacy classes of subgroups — too many to draw. Only its 30 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=g^2,b^a=b^2,d^a=d^2,e^a=e^2g,c^b=ce,d^b=df,e^b=eg93 conjugacy classes — view the full character table.
| maximal subgroup of | #72222201, #72222310 |
| maximal normal subgroup of | #72222310 |
| maximal quotient of | #72222194, #72222197, #72222261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1125);