Finite Group DatabasebetaFinite Group Databasebeta| order | 16900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C13⋊D13)⋊D25 |
| unambiguous semidirect product | D325⋊D13 |
| Fitting, derived, Hall | C132×C25 ⋊ C22 |
| Sylow | C132 ⋊ C2×D25 |
| Sylow | C25 ⋊ D132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C132×C25 | C22 |
| Frattini | C5 | D65⋊D13 |
| socle | C5×C132 | C2×D5 |
| LCS | G ▷ C132×C25 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 650 |
Polycyclic presentation:
2^2,5,13^2,5|c^5=f^4,c^a=c^4f,d^a=d^12,f^a=f^4,d^b=d^12,e^b=e^121096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16900, 80);