Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C9⋊SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C37 |
| direct product | C32×Q8⋊H(3,𝔽3) |
| Fitting | C34×Q8 ⋊ C3 |
| Sylow | Q8 ⋊ C32×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C33 | C3×A4 |
| commutator, cosocle | C3×Q8 | C34 |
| Frattini | C2×C3 | C33×A4 |
| Fitting | C34×Q8 | C3 |
| hypercenter | C2×C34 | A4 |
| hypocenter | Q8 | C32×H(3,𝔽3) |
| LCS | G ▷ C3×Q8 ▷ Q8 | |
| UCS | C1 ◁ C2×C33 ◁ C2×C34 | |
1562 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3265);