Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#64231 |
| Fitting | C2×C32×C4 ⋊ D4 |
| Sylow | C32 ⋊ C2×#127 |
734 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593155, #11776279, #11787886, … |
| maximal normal subgroup of | C2×#10593155, #11776279, #11787886, … |
| maximal quotient of | C2×#10593413, C2×#10593454, C2×#10593407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8391);