Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| direct product | C3×SL(2,𝔽3)⋊C16 |
| unambiguous semidirect product | SL(2,𝔽3)⋊(C3×C16) |
| derived | SL(2,𝔽3) ⋊ C3×C16 |
123 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 123 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C16×GL(2,𝔽3), C3×#72218959 |
| maximal normal subgroup of | C3×C16×GL(2,𝔽3) |
| maximal quotient of | C3×SL(2,𝔽3)⋊C32, C3×#72218959 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154136);