Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C3×#622 |
| derived | C32 ⋊ C22×C3×C8 |
| Sylow | C33 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | #157 |
| commutator, hypocenter | C32 | C22×C3×C8 |
| Frattini | C2 | C22×C3×#157 |
| Fitting, socle, prime radical | C23×C33 | C4 |
| cosocle | C3⋊Dic3 | C23×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C3 | |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13154847, C3×#10590075, #13155119, … |
| maximal normal subgroup of | #13154847, C3×#10590075, #13155119, … |
| maximal quotient of | C22×C3×#3708, C2×C3×#63773, C2×C3×C4×#622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4473);