Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×A4×ΓL(1,𝔽25) |
| unambiguous semidirect product | (C23×ΓL(1,𝔽25))⋊C3 |
| Fitting | C23×C3×C8 ⋊ C2×C3 |
822 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157310);