Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C37×#553 ⋊ C2 |
| Sylow | C37 ⋊ #3481 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D37 |
| commutator, socle, cosocle | C22×C37 | C25 |
| Fitting | C37×#553 | C2 |
| hypercenter | #553 | D37 |
| hypocenter | C37 | #3481 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #553 | |
1242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^7,37|e^2=fg,b^a=bf,c^a=cg,d^b=df,h^c=h^36,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, 18117);