Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C34 |
| direct product | C33×C4⋊(C3⋊D3) |
| unambiguous semidirect product | C4⋊(C33×C3⋊D3) |
| Fitting | C35×C4 ⋊ C2 |
| Sylow | C35 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C33 | C2×C3⋊D3 |
| commutator, cosocle | C2×C32 | C22×C33 |
| Frattini | C2 | C2×C33×C3⋊D3 |
| Fitting | C35×C4 | C2 |
| socle | C2×C35 | C22 |
| hypercenter | C33×C4 | C3⋊D3 |
| hypocenter | C32 | C33×D4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C33 ◁ C33×C4 | |
5088 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
567 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3853);