Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | SL(2,𝔽3)×Dic3⋊C4 |
| unambiguous semidirect product | Dic3⋊(C4×SL(2,𝔽3)) |
| unambiguous semidirect product | (Q8×Dic3⋊C4)⋊C3 |
421 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155274);