Finite Group DatabasebetaFinite Group Databasebeta| order | 552 |
| isoclinism | isoclinic class of D3×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D69⋊C4 |
| derived, Hall | C3×C23 ⋊ C2×C4 |
| Sylow | C23 ⋊ C4×D3 |
| Sylow | C3 ⋊ C4×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D23 |
| commutator, hypocenter | C3×C23 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C23 | C22 |
| prime radical | C2×D69 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 276 |
Polycyclic presentation:
2^3,3,23|a^2=c,b^2=c,e^a=e^22,d^b=d^278 conjugacy classes — view the full character table.
| maximal subgroup of | #11764226, D69⋊Q8, #11764230, … |
| maximal normal subgroup of | #11764226, D69⋊Q8, #11764230, … |
| maximal quotient of | D69⋊C8, #11764135, Dic3×Dic23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(552, 7);