Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×Q16×SL(2,𝔽3) |
| unambiguous semidirect product | (Q8×Q16)⋊C32 |
| unambiguous semidirect product | (C3×Q8×Q16)⋊C3 |
| Fitting | C3×Q8×Q16 ⋊ C3 |
| Sylow | Q8×Q16 ⋊ C32 |
320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153619);