Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C33 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×#157 |
| commutator, socle | C2×C33 | C2×C8 |
| Fitting | C33×C4 | C2×C4 |
| prime radical | C2×C32×D3 | C8 |
| cosocle | C3×C3⋊(C3⋊C8) | C22 |
| hypocenter | C33 | M32 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C4 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^5,3^3|b^2=c,c^2=d,d^2=e,b^a=be,h^a=h^2,f^b=g,g^b=f^2,f^c=f^2,g^c=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #13165360, #13165361, #13165364, … |
| maximal normal subgroup of | #13165360, #13165361, #13165364, … |
| maximal quotient of | #13154819, (C2×D3)⋊#3708, Dic3⋊#3708, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2687);