Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×#64146 |
| Fitting | C22×C32×D4 ⋊ C2 |
| Sylow | C32 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×C3⋊D3 |
| commutator, cosocle | C22×C32 | C24 |
| Frattini | C22 | C23×C3⋊D3 |
| Fitting | C22×C32×D4 | C2 |
| socle | C23×C32 | C23 |
| hypercenter | C22×D4 | C3⋊D3 |
| hypocenter | C32 | C2×#120 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
1986 conjugacy classes of subgroups; only the 295 normal subgroups are shown.
This group has 1986 conjugacy classes of subgroups — too many to draw. Only its 295 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11787924, #11787930, #11787944, … |
| maximal normal subgroup of | #11787924, #11787930, #11787944, … |
| maximal quotient of | C2×#10592654, C2×#10592688, C2×#10592645, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8152);