Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624765 ⋊ C2 |
| derived | C32⋊C9 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4169⋊C3 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C32 |
| Frattini | C33 | C32×D3 |
| Fitting | #10624765 | C2 |
| socle | C32 | C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
755 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 755 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.
| transitive degree | μt(G) = 18 |
Polycyclic presentation:
2,3^6|b^3=e,b^a=b^2e^2,e^a=e^2,f^a=f^2g,c^b=ce,d^b=df,f^b=fg93 conjugacy classes — view the full character table.
| maximal subgroup of | #72277518, #72277527 |
| maximal normal subgroup of | #72277527 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1243);