Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | D3×#3830 |
| Fitting | C33×D4 ⋊ C22 |
| Sylow | C33 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×C3⋊D3 |
| commutator, socle, cosocle | C2×C33 | C24 |
| Fitting | C33×D4 | C22 |
| hypercenter | D4 | D3×C3⋊D3 |
| hypocenter | C33 | C2×#41 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ D4 | |
1144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63783, #13166529, D3×#63927, … |
| maximal normal subgroup of | D3×#63783, #13166529, D3×#63927, … |
| maximal quotient of | #13175446, D3×#64086, #13175449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4551);