Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | D3×#504⋊C3 |
| unambiguous semidirect product | (D3×#504)⋊C3 |
| Fitting | C3×#504 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D3×A4 |
| commutator, hypocenter | C3×Q8 | C2×C3×C8 |
| Frattini | C8 | C2×D3×A4 |
| Fitting | C3×#504 | C2×C3 |
| socle | C2×C3 | C2×C8×A4 |
| prime radical | D3×#41⋊C3 | C4 |
| cosocle | C3×#131 | C22×C3 |
| LCS | G ▷ C3×Q8 | |
| UCS | C1 ◁ C16 | |
215 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 215 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155249);