Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C37×#520 ⋊ C2 |
| Sylow | C37 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D37 |
| commutator | C2×C37 | C24×C4 |
| Fitting | C37×#520 | C2 |
| socle, cosocle | C22×C37 | C25 |
| prime radical | C2×#41×D37 | C2 |
| hypercenter | #520 | D37 |
| hypocenter | C37 | #3428 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #520 | |
1540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^7,37|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^d=h^36,h^e=h^36680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 17710);