Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #131×C37 ⋊ C4 |
| Sylow | C37 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#3866 |
| commutator, socle | C2×C37 | C22×C42 |
| Fitting | #131×C37 | C4 |
| prime radical | #41×D37 | C22 |
| cosocle | C4×D37 | C24 |
| hypercenter | #131 | #3866 |
| hypocenter | C37 | #2875 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C4 ◁ #131 | |
556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^7,37|a^2=e,b^2=f,e^2=g,b^a=bg,h^b=h^31,d^c=dg,h^f=h^36248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 21080);