Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #108 |
89 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=de,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=fg,g^a=fg^2h^2,f^c=f^2,g^c=g^2h,g^f=gh58 conjugacy classes — view the full character table.
| maximal subgroup of | #13136660, #13136661, #13136724, … |
| maximal normal subgroup of | #13136660, #13136661, #13136724, … |
| maximal quotient of | #13136905, #13136906, #13136919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 744);