Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | SL(2,𝔽3)×#235 |
| unambiguous semidirect product | (Q8×#235)⋊C3 |
| Fitting | C2×C3×C4×Q8 ⋊ C2×C3 |
731 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 731 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157194);