Finite Group DatabasebetaFinite Group Databasebeta| order | 13780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D65⋊D53 |
| unambiguous semidirect product | D265⋊D13 |
| unambiguous semidirect product | D689⋊D5 |
| Fitting, socle, derived, Hall | C5×C13×C53 ⋊ C22 |
| Hall | C13×C53 ⋊ C2×D5 |
| Hall | C5×C53 ⋊ C2×D13 |
| Hall | C5×C13 ⋊ C2×D53 |
| Sylow | C53 ⋊ D5×D13 |
| Sylow | C13 ⋊ D5×D53 |
| Sylow | C5 ⋊ D13×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C53 | C22 |
| LCS | G ▷ C5×C13×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3445 |
Polycyclic presentation:
2^2,5,13,53|d^a=d^12,e^a=e^52,c^b=c^4,d^b=d^12916 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13780, 59);