Finite Group DatabasebetaFinite Group Databasebeta| order | 4384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#10587739 |
| unambiguous semidirect product | D137⋊(C22×C4) |
| Fitting, socle | C23×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10587739 |
| commutator, hypocenter | C137 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C137 | C4 |
| prime radical | C23×D137 | C2 |
| cosocle | D137 | C24 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C23 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1096 |
304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4384, 235);