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) ⋊ #107 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=cde,c^2=e,d^2=e,b^a=bc,f^a=gh^2,g^a=f^2,c^b=ce,d^b=de,f^b=f^2g^2,g^b=f^2gh^2,f^c=f^2h^2,g^c=g^2h,g^f=gh46 conjugacy classes — view the full character table.
| maximal subgroup of | #13146173, #13146174, #13146711, … |
| maximal normal subgroup of | #13146173, #13146174, #13146711, … |
| maximal quotient of | #13136725, #13136726, #13136727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 677);