Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C33×C4 ⋊ C2×C4 |
| Sylow | C33 ⋊ C4×D4 |
328 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^5,3^3|b^2=d,c^2=e,c^a=ce,h^a=h^2,c^b=ce,f^b=g,g^b=f^2,f^d=f^2,g^d=g^248 conjugacy classes — view the full character table.
| maximal subgroup of | #13165257, #13165263, #13165269, … |
| maximal normal subgroup of | #13165257, #13165263, #13165269, … |
| maximal quotient of | #13166253, #13166254, #13166255, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4226);