Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×D9 |
| commutator | C2×C3×C9 | C42 |
| Frattini | C23×C3 | D32 |
| Fitting, cosocle | C23×C3×C9 | C22 |
| socle, prime radical | C23×C32 | C2×D3 |
| hypocenter | C3×C9 | #95 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C23 | |
282 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=c,f^3=h,b^a=be,g^a=g^2,f^b=f^2h^2,h^b=h^2132 conjugacy classes — view the full character table.
| maximal subgroup of | #13139424, #13139425, #13139426, … |
| maximal normal subgroup of | #13139424, #13139425, #13139426, … |
| maximal quotient of | #13135118, #13135119, #13135120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 298);