Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×C4×#216 |
| Sylow | C32 ⋊ C4×Q16 |
255 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#68213, C3×C8×#216, C3⋊C8×#216, … |
| maximal normal subgroup of | C3×#68213, C3×C8×#216, C3⋊C8×#216, … |
| maximal quotient of | C3×C8×#216, C3×#70956, C3×#70934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4008);