Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | D3×C8×Dic3 |
| derived, Sylow | C32 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D32 |
| commutator, hypocenter | C32 | C2×C4×C8 |
| Frattini | C2×C4 | C2×D32 |
| Fitting | C2×C32×C8 | C22 |
| socle | C22×C32 | C22×C4 |
| prime radical | C22×C3×D3 | C2×C4 |
| cosocle | C2×C32×C4 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C8 | |
346 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Dic3×C16, D3×#4502, #11795860, … |
| maximal normal subgroup of | D3×Dic3×C16, D3×#4502, #11795860, … |
| maximal quotient of | D3×C8×C3⋊C8, D3×#4454, C8×#3711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2535);