Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C23 · Schur multiplier (H2) = C3 |
| Fitting | C3×Q8×C23 ⋊ C3 |
| derived, Sylow | Q8 ⋊ C32×C23 |
| Hall | Q8×C23 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3×C23 | A4 |
| commutator, cosocle, hypocenter | Q8 | C32×C23 |
| Frattini | C2 | C3×A4×C23 |
| Fitting | C3×Q8×C23 | C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C3×C23 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 552 |
483 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 79);