Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C37×#554 ⋊ C2 |
| Sylow | C37 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D37 |
| commutator, socle, cosocle | C22×C37 | C25 |
| Fitting | C37×#554 | C2 |
| prime radical | C2×#10596964 | C22 |
| hypercenter | #554 | D37 |
| hypocenter | C37 | Q8×#41 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #554 | |
1068 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^7,37|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^d=h^36,h^e=h^36500 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 18089);