Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×C4×D32 |
| Fitting | C22×C32×C4 ⋊ C22 |
| derived, Sylow | C32 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D32 |
| commutator, hypocenter | C32 | C24×C4 |
| Frattini | C2 | C23×D32 |
| Fitting | C22×C32×C4 | C22 |
| socle | C23×C32 | C23 |
| prime radical | C23×D32 | C2 |
| cosocle | C2×C32 | C25 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C4 | |
2842 conjugacy classes of subgroups; only the 944 normal subgroups are shown.
This group has 2842 conjugacy classes of subgroups — too many to draw. Only its 944 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8544);