Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6249 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#6249 |
| Fitting | C4×H(3,𝔽3) ⋊ C8 |
| derived, Sylow | H(3,𝔽3) ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #6249 |
| commutator, hypocenter | H(3,𝔽3) | C4×C8 |
| Frattini, socle | C2×C3 | C2×AGL(1,𝔽9) |
| Fitting | C4×H(3,𝔽3) | C8 |
| prime radical | C2×#272 | C2×C4 |
| cosocle | C2×#1088 | C22 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C4 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | #6249⋊C8, (#1088⋊C2)⋊C8, SU(3,𝔽2)⋊C8, … |
| maximal normal subgroup of | #6249⋊C8, (#1088⋊C2)⋊C8, SU(3,𝔽2)⋊C8, … |
| maximal quotient of | C8×#6249, #13146429, #13146432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2256);