Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×C8×C3⋊(C3⋊D3) |
| Fitting | C2×C33×C8 ⋊ C2 |
| derived, Sylow | C33 ⋊ C22×C8 |
1064 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | #13145553, #13146052, C2×#11722000, … |
| maximal normal subgroup of | #13145553, #13146052, C2×#11722000, … |
| maximal quotient of | C8×#6308, C4×C8×C3⋊(C3⋊D3), #13163325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3907);