Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×D108 |
| unambiguous semidirect product | C4⋊(C32×D27) |
| Fitting | C32×C4×C27 ⋊ C2 |
| Sylow | C32×C27 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C32 | C2×D27 |
| commutator, cosocle | C2×C27 | C22×C32 |
| Frattini | C2×C9 | C2×C32×D3 |
| Fitting | C32×C4×C27 | C2 |
| socle | C2×C33 | C2×D9 |
| hypercenter | C32×C4 | D27 |
| hypocenter | C27 | C32×D4 |
| LCS | G ▷ C2×C27 ▷ C27 | |
| UCS | C1 ◁ C2×C32 ◁ C32×C4 | |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1731);