Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×C32×Dic3 |
| derived | C3 ⋊ C23×C32×C4 |
| Sylow | C33 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C32 | D3 |
| commutator, hypocenter | C3 | C23×C32×C4 |
| Frattini | C2 | C23×C32×D3 |
| Fitting, socle, prime radical | C24×C33 | C2 |
| cosocle | C2×C3 | C24×C32 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C24×C32 | |
1952 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#63579, C3×#10591696, C3×Dic3×#217, … |
| maximal normal subgroup of | C2×C3×#63579, C3×#10591696, C3×Dic3×#217, … |
| maximal quotient of | C23×C32×C3⋊C8, C22×C32×#208, C22×C32×C4×Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4623);