Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ SD32 |
101 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 101 conjugacy classes of subgroups — too many to draw. Only its 26 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|b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,g^a=g^2,h^a=h^2,c^b=cd,d^b=de,f^b=f^2,h^b=h^2,g^f=gh49 conjugacy classes — view the full character table.
| maximal subgroup of | #13137002, #13137003, #13137006, … |
| maximal normal subgroup of | #13137002, #13137003, #13137006, … |
| maximal quotient of | #13135081, #13135083, #13135087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 216);