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×C4⋊#226 |
| unambiguous semidirect product | C4⋊(C3×#226) |
145 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 145 conjugacy classes of subgroups — too many to draw. Only its 34 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 | #11920501, #11920506, #11920528, … |
| maximal normal subgroup of | #11920501, #11920506, #11920528, … |
| maximal quotient of | C3×#73012, C3×#73013, C3×#73014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5458);