Finite Group DatabasebetaFinite Group Databasebeta| order | 552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C23 ⋊ Q8 |
| Sylow | C23 ⋊ Dic6 |
| Sylow | C3 ⋊ Dic46 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D23 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C3×C23 | C22 |
| hypocenter | C3×C23 | Q8 |
| LCS | G ▷ C2×C3×C23 ▷ C3×C23 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 552 |
Polycyclic presentation:
2^3,3,23|a^2=c,b^2=c,b^a=bc,e^a=e^22,d^b=d^275 conjugacy classes — view the full character table.
| maximal subgroup of | Dic6×D23, D3×Dic46, D69⋊Q8, … |
| maximal normal subgroup of | Dic6×D23, D3×Dic46, D69⋊Q8, … |
| maximal quotient of | Dic23⋊Dic3, #11764153, Dic3⋊Dic23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(552, 11);