Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #6882⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#6882⋊C2 |
| Fitting, Sylow | C3×#6882 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #6882⋊C2 |
| commutator, cosocle, hypocenter | #733 | C2×C32 |
| Frattini | C3×C9 | C32×D3 |
| Fitting | C3×#6882 | C2 |
| socle | C32 | #4178 |
| prime radical | C3×#733⋊C2 | C3 |
| LCS | G ▷ #733 | |
| UCS | C1 ◁ C3 | |
113 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | #72222263, C3×(#6880⋊C2)⋊C3 |
| maximal normal subgroup of | C3×(#6880⋊C2)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1382);