Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#5425 |
161 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 161 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | #11922282, #11922288, #11922291, … |
| maximal normal subgroup of | #11922282, #11922288, #11922291, … |
| maximal quotient of | C3×#73059, C3×#73061, C3×#73089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5493);