Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C3⋊D3×AGL(1,ℤ/8) |
| Fitting | C32×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C32 ⋊ C2×AGL(1,ℤ/8) |
894 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #11787729, #11788623, AGL(1,ℤ/8)×#157, … |
| maximal normal subgroup of | #11787729, #11788623, AGL(1,ℤ/8)×#157, … |
| maximal quotient of | C3⋊D3×#418, C3⋊D3×#417, C3⋊D3×#428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8125);