Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C33×GO+(4,𝔽2) |
| unambiguous semidirect product | #157⋊(C2×C33) |
| unambiguous semidirect product | D32⋊(C2×C33) |
| Fitting, socle, Sylow | C35 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | GO+(4,𝔽2) |
| commutator, cosocle | C3⋊D3 | C22×C33 |
| Frattini | C1 | G |
| Fitting, socle | C35 | D4 |
| hypocenter | C32 | C33×D4 |
| LCS | G ▷ C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C33 | |
1508 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3907);