Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C3×C4×GU(2,𝔽3) |
| derived | SL(2,𝔽3) ⋊ C3×C42 |
369 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154855);