Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C33 |
No aliases for this group.
| Sylow | C33 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×C3⋊(C3⋊D3) |
| commutator, socle | C2×C33 | C22×C4 |
| Fitting, prime radical | C33×#41 | C2 |
| cosocle | C33×C4 | C23 |
| hypercenter | #41 | C3⋊(C3⋊D3) |
| hypocenter | C33 | #131 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C4 ◁ #41 | |
868 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|a^2=d,d^2=e,f^a=f^2,g^a=g^2,h^a=h^2,c^b=ce150 conjugacy classes — view the full character table.
| maximal subgroup of | #13161373, #13161374, #13161375, … |
| maximal normal subgroup of | #13161373, #13161374, #13161375, … |
| maximal quotient of | #13163636, #13163639, #13163640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3956);