Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Fitting | C37×#322 ⋊ C2 |
| Sylow | C37 ⋊ #1455 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D37 |
| commutator, socle | C22×C37 | C2×C42 |
| Fitting | C37×#322 | C2 |
| prime radical | C22×D37 | C42 |
| cosocle | C42×C37 | C23 |
| hypercenter | #322 | D37 |
| hypocenter | C37 | #1455 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C42 ◁ #322 | |
214 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^7,37|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cf,c^b=cg,h^b=h^36,h^c=h^36776 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 2814);