Finite Group DatabasebetaFinite Group Databasebeta| order | 552 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C23⋊C8) |
| unambiguous semidirect product | C23⋊(C3⋊C8) |
| derived, Hall | C3×C23 ⋊ C8 |
| Sylow | C23 ⋊ C3⋊C8 |
| Sylow | C3 ⋊ C23⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D69 |
| commutator, hypocenter | C3×C23 | C8 |
| Fitting, cosocle | C3×C4×C23 | C2 |
| socle, prime radical | C2×C3×C23 | C4 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 552 |
Polycyclic presentation:
2^3,3,23|a^2=b,b^2=c,d^a=d^2,e^a=e^22144 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×D23, D3×C23⋊C8, #11764133, … |
| maximal normal subgroup of | C3⋊C8×D23, D3×C23⋊C8, #11764133, … |
| maximal quotient of | C3⋊(C23⋊C16), C2×C3⋊(C23⋊C8), C9⋊(C23⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(552, 3);