Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C37 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#3866 |
| commutator, socle | C2×C37 | C22×C16 |
| Fitting | M32×C37 | C4 |
| prime radical | #10596962 | C8 |
| cosocle | #10596925 | C23 |
| hypercenter | M32 | #3866 |
| hypocenter | C37 | #2258 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C8 ◁ M32 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^7,37|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^31,c^b=cg,h^b=h^36,h^d=h^36260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 20934);