Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #63419 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#63419 |
| derived | C42⋊C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #63419 |
| commutator, cosocle, hypocenter | C42⋊C9 | C2×C3 |
| Frattini | C22×C3 | C3×S4 |
| Fitting | C32×C42 | D3 |
| socle | C22×C32 | S4 |
| LCS | G ▷ C42⋊C9 | |
| UCS | C1 ◁ C3 | |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 72 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63419, #63419⋊D3, C2×C3×#63419, … |
| maximal normal subgroup of | D3×#63419, #63419⋊D3, C2×C3×#63419, … |
| maximal quotient of | C3×#10588301, C3×#10588302, C3×#10588303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 685);