Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | H(5,𝔽2) ⋊ 3−1+2 |
232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
3^3,2^5|a^3=c,b^a=bc,d^a=e,e^a=de,f^a=g,g^a=fg,g^d=gh,f^e=fh67 conjugacy classes — view the full character table.
| maximal subgroup of | #13141257, #13141260, #13164526, … |
| maximal normal subgroup of | #13141257, #13141260, #13164526, … |
| maximal quotient of | #13152257, #13152260, #13152265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2556);