Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×C3×#157 |
| Fitting, socle | C23×C33 ⋊ C4 |
| derived | C32 ⋊ C23×C3×C4 |
| Sylow | C33 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | #157 |
| commutator, hypocenter | C32 | C23×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C33 | C4 |
| prime radical | C23×C3×C3⋊D3 | C2 |
| cosocle | C3⋊D3 | C24×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C3 | |
804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11722722, #157×#217, #13166605, … |
| maximal normal subgroup of | C2×#11722722, #157×#217, #13166605, … |
| maximal quotient of | C22×C3×#3787, C22×C3×#3788, C2×C3×#64283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4715);