Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #101 |
115 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=d,d^2=e,b^a=bc,d^a=de,f^a=f^2,g^a=gh,h^a=h^2,c^b=ce,f^b=gh^2,g^b=fh^2,h^b=h^2,f^c=f^2,g^c=g^2h^2,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | #13146478, #13146480, #13146482, … |
| maximal normal subgroup of | #13146478, #13146480, #13146482, … |
| maximal quotient of | #13136674, #13136676, #13136682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 667);