Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ M32 |
55 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=e,c^2=d,d^2=e,b^a=be,f^a=f^2g^2,g^a=f^2h^2,h^a=h^2,f^c=f^2g,g^c=fgh^2,f^d=f^2,g^d=g^2h^2,g^f=gh40 conjugacy classes — view the full character table.
| maximal subgroup of | #13146171, #13146172, #13146434, … |
| maximal normal subgroup of | #13146171, #13146172, #13146434, … |
| maximal quotient of | #13146439, #13146440, C4⋊#88586, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2255);