Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C2×C3×C4×C3⋊Dic3 |
| derived | C32 ⋊ C2×C3×C42 |
| Sylow | C33 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C4 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C3×C42 |
| Frattini | C22 | C22×C3×C3⋊D3 |
| Fitting | C22×C33×C4 | C2 |
| socle, prime radical | C23×C33 | C22 |
| cosocle | C22×C32 | C23×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C3×C4 | |
864 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 378 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10589156, C3×#10589160, #13145639, … |
| maximal normal subgroup of | C3×#10589156, C3×#10589160, #13145639, … |
| maximal quotient of | C2×C3×C4×C3⋊(C3⋊C8), C2×C3×#63630, C3×C4×#3748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3844);