Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#859 |
| derived | SL(2,𝔽3) ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C9 | S4 |
| commutator, hypocenter | SL(2,𝔽3) | C4×C9 |
| Frattini, socle | C22×C3 | C3×S4 |
| Fitting | C2×Q8×C9 | D3 |
| prime radical, cosocle | C2×C3×SL(2,𝔽3) | C2×C3 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C22×C9 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13146205, #13146207, #13146208, … |
| maximal normal subgroup of | #13146205, #13146207, #13146208, … |
| maximal quotient of | C9×SL(2,𝔽3)⋊C8, C2×C9×#859 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 682);