Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | C4⋊(C3⋊(C3⋊(C3⋊C8))) |
| Sylow | C33 ⋊ C4⋊C8 |
532 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=f^2,g^a=g^2,h^a=h^2228 conjugacy classes — view the full character table.
| maximal subgroup of | #13145507, #13145509, #13145513, … |
| maximal normal subgroup of | #13145507, #13145509, #13145513, … |
| maximal quotient of | #13146002, #13146003, C4⋊(C3⋊(C3⋊(C3⋊C16))), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2141);