Finite Group DatabasebetaFinite Group Databasebeta| order | 4384 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#11764049 |
| unambiguous semidirect product | #10587739⋊C8 |
| Fitting | C4×C137 ⋊ C8 |
| derived, Sylow | C137 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #11764049 |
| commutator, hypocenter | C137 | C4×C8 |
| Frattini | C2 | C2×#11764049 |
| Fitting | C4×C137 | C8 |
| socle | C2×C137 | C2×C8 |
| prime radical | C2×D137 | C2×C4 |
| cosocle | C2×#10587739 | C22 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 548 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4384, 237);