Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10624887⋊C2 |
| Fitting, Sylow | #10624887 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4207⋊C3 |
| commutator, cosocle | C32×C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624887 | C2 |
| prime radical | C3×#4207 | C3 |
| hypocenter | C3×C9 | C2×3−1+2 |
| LCS | G ▷ C32×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C3 | |
263 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=g,e^3=f,c^a=c^2,e^a=e^2f^2,f^a=f^2,c^b=cf,d^b=dg,e^b=ef,d^c=df69 conjugacy classes — view the full character table.
| maximal subgroup of | #72221842, #72221843, #72221844, … |
| maximal normal subgroup of | #72221845, #72243277, C2×#10624887⋊C2 |
| maximal quotient of | #72243268, #72243270, #72243893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1560);