Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C2×C33×C4 ⋊ C22 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
1008 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|c^2=d,c^a=ce,h^a=h^2,c^b=ce,f^b=f^2,g^b=g^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #13168136, #13168147, #13168148, … |
| maximal normal subgroup of | #13168136, #13168147, #13168148, … |
| maximal quotient of | #13159049, #13159050, #13159065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3506);