Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#64239 |
| Sylow | C32 ⋊ C2×#137 |
418 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #11787707, #11788551, #11792174, … |
| maximal normal subgroup of | #11787707, #11788551, #11792174, … |
| maximal quotient of | C2×#10593503, C2×#10593496, C2×#10593507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8416);