Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C33 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×#157 |
| commutator, socle | C2×C33 | C42 |
| Fitting | C33×C4 | C2×C4 |
| prime radical | C2×C3×C3⋊D3 | C2×C4 |
| cosocle | C3×C4×C3⋊D3 | C22 |
| hypocenter | C33 | #97 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C4 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=c,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 | #13165175, #13165178, #13165189, … |
| maximal normal subgroup of | #13165175, #13165178, #13165189, … |
| maximal quotient of | #13154733, #13154763, #13154764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2671);