Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C32×C23 ⋊ Q8 |
| Sylow | C23 ⋊ #627 |
| Sylow | C32 ⋊ Dic46 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C3⋊D3)⋊D23 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C32×C23 | C22 |
| hypocenter | C32×C23 | Q8 |
| LCS | G ▷ C2×C32×C23 ▷ C32×C23 | |
| UCS | C1 ◁ C2 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 552 |
Polycyclic presentation:
2^3,3^2,23|a^2=c,b^2=c,b^a=bc,d^a=d^2,f^a=f^22,d^b=d^2,e^b=e^2147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 78);