Finite Group DatabasebetaFinite Group Databasebeta| order | 5382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(D13⋊C9) |
| unambiguous semidirect product | (C13⋊C9)⋊D23 |
| unambiguous semidirect product | D299⋊C9 |
| derived, Hall | C13×C23 ⋊ C2×C9 |
| Hall | C23×C13⋊C9 ⋊ C2 |
| Hall | D299 ⋊ C9 |
| Hall | C13⋊C9 ⋊ D23 |
| Sylow | C23 ⋊ D13⋊C9 |
| Sylow | C13 ⋊ C9×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C23⋊(D13⋊C3) |
| commutator, hypocenter | C13×C23 | C2×C9 |
| Fitting, socle | C3×C13×C23 | C2×C3 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,23,3|b^3=e,c^a=c^12,d^a=d^22,c^b=c^9255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5382, 4);