Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×SL(2,ℤ/4)⋊C4 |
| unambiguous semidirect product | SL(2,ℤ/4)⋊(C3×C4) |
234 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #11921884, #11921890, #11921893, … |
| maximal normal subgroup of | #11921884, #11921890, #11921893, … |
| maximal quotient of | C3×#73050, C3×#73051, C3×#73059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5479);