Finite Group DatabasebetaFinite Group Databasebeta| order | 552 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×Dic23 |
| unambiguous semidirect product | (C2×C23)⋊(C3×C4) |
| derived, Sylow | C23 ⋊ C2×C3×C4 |
| Hall | C3×C23 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D23 |
| commutator, hypocenter | C23 | C2×C3×C4 |
| Frattini | C2 | C2×C3×D23 |
| Fitting, socle, prime radical | C22×C3×C23 | C2 |
| cosocle | C2×C23 | C22×C3 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C22×C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 552 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×Dic23, (C2×D3)⋊Dic23, #11764151, … |
| maximal normal subgroup of | Dic3×Dic23, (C2×D3)⋊Dic23, #11764151, … |
| maximal quotient of | C2×C3×C23⋊C8, C3×#67267, C3×C4×Dic23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(552, 16);