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 |
143 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^2,g^a=g^2,g^f=gh124 conjugacy classes — view the full character table.
| maximal subgroup of | #13135089, #13135090, #13135091, … |
| maximal normal subgroup of | #13135089, #13135090, #13135091, … |
| maximal quotient of | #13135751, C4⋊#88386, #13135930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 512);