Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3714 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#63573 |
| Sylow | C32 ⋊ C2×#106 |
306 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #11784441, Dic3×#808, #11784444, … |
| maximal normal subgroup of | #11784441, Dic3×#808, #11784444, … |
| maximal quotient of | C2×#10589097, #11776877, #11776988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3005);