Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×#226 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×S4 |
| commutator, cosocle, hypocenter | C3×SL(2,𝔽3) | C23 |
| Frattini | C2 | C2×D3×S4 |
| Fitting | C2×C3×Q8 | C2×D3 |
| socle | C22×C3 | C2×S4 |
| prime radical | C2×D3×SL(2,𝔽3) | C2 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C22 | |
319 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#226, D3×#5388, #11921677, … |
| maximal normal subgroup of | C4×D3×#226, D3×#5388, #11921677, … |
| maximal quotient of | Dic6×#226, #11921476, #11921477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8320);