Finite Group DatabasebetaFinite Group Databasebeta| order | 552 |
| isoclinism | isoclinic class of D3×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×D23 |
| unambiguous semidirect product | (D3×C23)⋊C22 |
| unambiguous semidirect product | (C3×D23)⋊C22 |
| unambiguous semidirect product | D69⋊C22 |
| Fitting, socle | C2×C3×C23 ⋊ C22 |
| derived, Hall | C3×C23 ⋊ C23 |
| Sylow | C23 ⋊ C22×D3 |
| Sylow | C3 ⋊ C22×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D23 |
| commutator, cosocle, hypocenter | C3×C23 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C23 | C22 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 138 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×D23, D12×D23, D3×D92, … |
| maximal normal subgroup of | C4×D3×D23, D12×D23, D3×D92, … |
| maximal quotient of | Dic6×D23, #11764222, #11764223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(552, 34);