Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C8×C3⋊GL(2,𝔽3) |
| Fitting | C3×C8×Q8 ⋊ D3 |
| derived | C3×SL(2,𝔽3) ⋊ C2×C8 |
352 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154984);