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 |
165 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bd,f^a=f^2,g^a=g^2,d^b=de,g^f=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #13139163, #13139164, #13139167, … |
| maximal normal subgroup of | #13139163, #13139164, #13139167, … |
| maximal quotient of | #13135794, #13135795, #13135947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 526);