Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of (C3⋊D3)⋊D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D69⋊Dic3 |
| derived, Hall | C32×C23 ⋊ C2×C4 |
| Sylow | C23 ⋊ D3×Dic3 |
| Sylow | C32 ⋊ C4×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C3⋊D3)⋊D23 |
| commutator, hypocenter | C32×C23 | C2×C4 |
| Fitting, socle, cosocle | C2×C32×C23 | C22 |
| prime radical | C2×C3×D69 | C2 |
| LCS | G ▷ C32×C23 | |
| UCS | C1 ◁ C2 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 552 |
Polycyclic presentation:
2^3,3^2,23|b^2=c,d^a=d^2,f^a=f^22,d^b=d^2,e^b=e^2150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 74);