Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #13133353⋊C3 |
| Fitting, socle, derived, Hall | C52×C17 ⋊ C3×C4 |
| Hall | #13133353 ⋊ C3 |
| Hall | C17×C52⋊C3 ⋊ C4 |
| Hall | C52⋊C3 ⋊ #595 |
| Sylow | C52 ⋊ C3×#595 |
| Sylow | C17 ⋊ #1039⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C17 | C3×C4 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5^2,17|a^2=c,d^a=d^4,e^a=e^4,f^a=f^13,d^b=de,e^b=d^2e^3,f^c=f^1664 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 68);