Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×D37⋊C32 |
| unambiguous semidirect product | D37⋊(C2×C32) |
| derived, Sylow | C37 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #3866 |
| commutator, hypocenter | C37 | C22×C32 |
| Frattini | C8 | C22×#3866 |
| Fitting | C2×C16×C37 | C4 |
| socle | C22×C37 | C2×C16 |
| prime radical | C22×D37 | C16 |
| cosocle | #10596925 | C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C16 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 20929);