Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^2,3^3,2^3|a^2=h,b^2=h,c^3=e,f^2=h,g^2=h,b^a=bh,c^a=c^2e^2,d^a=d^2,e^a=e^2,f^a=gh,g^a=fh,f^c=g,g^c=fgh,g^f=gh69 conjugacy classes — view the full character table.
| maximal subgroup of | #13146355, #13146360, #13146366, … |
| maximal normal subgroup of | #13146355, #13146360, #13146366, … |
| maximal quotient of | #13146990, #13146992, C4⋊(C3⋊#3688), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2356);