Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C3×C4 |
| direct product | C8×C3⋊Dic9 |
| derived, Sylow | C3×C9 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | C3⋊D9 |
| commutator, hypocenter | C3×C9 | C4×C8 |
| Frattini | C2×C3×C4 | C2×C3⋊D3 |
| Fitting | C2×C3×C8×C9 | C2 |
| socle, prime radical | C22×C32 | C4×D3 |
| cosocle | C2×C3×C4×C9 | C22 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C2×C8 | |
220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | #13135012, #13135014, #13135016, … |
| maximal normal subgroup of | #13135012, #13135014, #13135016, … |
| maximal quotient of | C8×C3⋊(C9⋊C8), #13135735, C16×C3⋊Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 503);