Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ C22⋊C8 |
275 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=c,c^2=e,b^a=bd,f^a=f^2,g^a=g^2,g^f=gh124 conjugacy classes — view the full character table.
| maximal subgroup of | #13135154, #13135155, #13135156, … |
| maximal normal subgroup of | #13135154, #13135155, #13135156, … |
| maximal quotient of | #13135877, #13135881, #13135887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 540);