Finite Group DatabasebetaFinite Group Databasebeta| order | 552 |
| isoclinism | isoclinic class of A4×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×D23 |
| unambiguous semidirect product | C23⋊(C2×A4) |
| unambiguous semidirect product | (C22×D23)⋊C3 |
| Fitting, socle, derived | C22×C23 ⋊ C2×C3 |
| Hall | C22×D23 ⋊ C3 |
| Sylow | C23 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C23 | C2×C3 |
| LCS | G ▷ C22×C23 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 92 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D23, C2×A4×D23, C3×A4×D23, … |
| maximal normal subgroup of | S4×D23, C2×A4×D23, C3×A4×D23, … |
| maximal quotient of | C23⋊(#41⋊C3), SL(2,𝔽3)×D23, A4×Dic23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(552, 33);