Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
| direct product | D9×#737 |
| Fitting, Sylow | C9×#737 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C9 | C32×D9 |
| commutator, cosocle | C3×C9 | C2×C33 |
| Frattini, socle | C32 | C33×D3 |
| Fitting | C9×#737 | C2 |
| prime radical | D9×H(3,𝔽3) | C3 |
| hypercenter | #737 | D9 |
| hypocenter | C9 | C2×#737 |
| LCS | G ▷ C3×C9 ▷ C9 | |
| UCS | C1 ◁ C9 ◁ #737 | |
395 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | #72243254, D9×#4207 |
| maximal normal subgroup of | #72243254, D9×#4207 |
| maximal quotient of | C9×D9×3−1+2, D9×#6894, D9×C9⋊H(3,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1448);