Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C25×#3866 |
| unambiguous semidirect product | D37⋊(C24×C4) |
| Fitting, socle | C25×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #3866 |
| commutator, hypocenter | C37 | C25×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C37 | C4 |
| prime radical | C25×D37 | C2 |
| cosocle | D37 | C26 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C25 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 21507);