Finite Group DatabasebetaFinite Group Databasebeta| order | 1776 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #41⋊(C37⋊C3) |
| Fitting, Hall | #41×C37 ⋊ C3 |
| Sylow | C37 ⋊ #41⋊C3 |
| Sylow | #41 ⋊ C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C22⋊(C37⋊C3) |
| commutator, cosocle, hypocenter | Q8×C37 | C2×C3 |
| Frattini | C2 | C2×C22⋊(C37⋊C3) |
| Fitting | #41×C37 | C3 |
| socle | C2×C37 | C2×A4 |
| LCS | G ▷ Q8×C37 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2,3,2^2,37,2|a^2=f,c^2=f,d^2=f,c^b=cd,d^b=c,e^b=e^10,d^c=df134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1776, 203);