Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C8×C3⋊D3 |
| Fitting | C22×C32×C8 ⋊ C2 |
| derived, Sylow | C32 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | C3⋊D3 |
| commutator, hypocenter | C32 | C23×C8 |
| Frattini | C4 | C23×C3⋊D3 |
| Fitting | C22×C32×C8 | C2 |
| socle | C23×C32 | C2×C4 |
| prime radical | C23×C3⋊D3 | C4 |
| cosocle | C32×C4 | C24 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C8 | |
1014 conjugacy classes of subgroups; only the 359 normal subgroups are shown.
This group has 1014 conjugacy classes of subgroups — too many to draw. Only its 359 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#336, C2×#10590181, #11783065, … |
| maximal normal subgroup of | C3⋊D3×#336, C2×#10590181, #11783065, … |
| maximal quotient of | C2×C4×C8×C3⋊D3, C22×C8×C3⋊Dic3, C2×C3⋊D3×C22⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8089);