Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#64204 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×S4 |
| commutator, cosocle | C2×C3×A4 | C23 |
| Frattini | C2 | C2×D3×S4 |
| Fitting, socle | C24×C3 | C2×D3 |
| prime radical | C22×C3×A4 | C22 |
| hypocenter | C3×A4 | C2×Q8 |
| LCS | G ▷ C2×C3×A4 ▷ C3×A4 | |
| UCS | C1 ◁ C22 | |
346 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#64204, #11921951, #11921952, … |
| maximal normal subgroup of | C4×#64204, #11921951, #11921952, … |
| maximal quotient of | #11921902, #11921910, #11921914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8343);