Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#64141 |
| Fitting | C22×C32×D4 ⋊ C2 |
| Sylow | C32 ⋊ C2×AGL(1,ℤ/8) |
894 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 231 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | #11787709, #11787727, #11787740, … |
| maximal normal subgroup of | #11787709, #11787727, #11787740, … |
| maximal quotient of | C2×#10592914, C2×#10592665, C2×#10592663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8146);