Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | D3×#399⋊C3 |
| unambiguous semidirect product | (D3×#399)⋊C3 |
| Fitting | C3×#399 ⋊ C2×C3 |
| derived | C3×#95 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#127⋊C3 |
| commutator, cosocle, hypocenter | C3×#95 | C22×C3 |
| Frattini | C23 | C2×D3×A4 |
| Fitting | C3×#399 | C2×C3 |
| socle | C23×C3 | C22×A4 |
| LCS | G ▷ C3×#95 | |
| UCS | C1 ◁ C2 | |
438 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155205);