Finite Group DatabasebetaFinite Group Databasebeta| order | 552 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×D23 |
| unambiguous semidirect product | C23⋊(C23×C3) |
| unambiguous semidirect product | (C2×C23)⋊(C22×C3) |
| Fitting, socle | C22×C3×C23 ⋊ C2 |
| derived, Sylow | C23 ⋊ C23×C3 |
| Hall | C3×C23 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D23 |
| commutator, cosocle, hypocenter | C23 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C23 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C22×C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 276 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D23)⋊Dic3, C3×(C2×D23)⋊C4, C2×Dic3×D23, … |
| maximal normal subgroup of | (C2×D23)⋊Dic3, C3×(C2×D23)⋊C4, C2×Dic3×D23, … |
| maximal quotient of | C2×C3×Dic46, C2×C3×C4×D23, C2×C3×D92, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(552, 36);