Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C33 |
| direct product | C23×C3⋊(C3⋊Dic3) |
| derived, Sylow | C33 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | C3⋊(C3⋊D3) |
| commutator, hypocenter | C33 | C23×C4 |
| Frattini | C2 | C23×C3⋊(C3⋊D3) |
| Fitting, socle, prime radical | C24×C33 | C2 |
| cosocle | C2×C33 | C24 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C24 | |
3304 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11722061, #13161409, #13161416, … |
| maximal normal subgroup of | C2×#11722061, #13161409, #13161416, … |
| maximal quotient of | C23×C3⋊(C3⋊(C3⋊C8)), C22×#88855, C22×C4×C3⋊(C3⋊Dic3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4653);