Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C2×Dic3×#157 |
| derived, Sylow | C33 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×#157 |
| commutator, hypocenter | C33 | C2×C42 |
| Frattini | C2 | C2×D3×#157 |
| Fitting, socle | C22×C33 | C2×C4 |
| prime radical | C22×C3×C3⋊D3 | C22 |
| cosocle | C2×C3×C3⋊D3 | C23 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C22 | |
356 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #13165061, Dic3×D32⋊C4, #13165370, … |
| maximal normal subgroup of | #13165061, Dic3×D32⋊C4, #13165370, … |
| maximal quotient of | #13166279, C2×C3⋊C8×#157, #157×#208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4227);