Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊C8×SL(2,𝔽3) |
| unambiguous semidirect product | (C2×C3)⋊(C8×SL(2,𝔽3)) |
| unambiguous semidirect product | (C2×Q8×C3⋊C8)⋊C3 |
| derived | C3×Q8 ⋊ C2×C3×C8 |
345 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155269);