Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C33 ⋊ #108 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=cd,c^2=e,b^a=bcd,d^a=de,f^a=g,g^a=f^2,h^a=h^2,f^b=fg^2,g^b=f^2g^2,f^c=f^2,g^c=g^242 conjugacy classes — view the full character table.
| maximal subgroup of | #13165102, #13165103, #13165104, … |
| maximal normal subgroup of | #13165102, #13165103, #13165104, … |
| maximal quotient of | #13155157, #13155159, #13155176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2778);