Finite Group DatabasebetaFinite Group Databasebeta| order | 16900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| derived, Hall | C132×C25 ⋊ C4 |
| Sylow | C132 ⋊ Dic25 |
| Sylow | C25 ⋊ #10621725 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊D325 |
| commutator, hypocenter | C132×C25 | C4 |
| Frattini | C2×C5 | C5⋊(C13⋊D13) |
| Fitting, cosocle | C2×C132×C25 | C2 |
| socle, prime radical | C2×C5×C132 | D5 |
| LCS | G ▷ C132×C25 | |
| UCS | C1 ◁ C2 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16900 |
Polycyclic presentation:
2,5,13^2,2,5|a^2=e,b^5=f^4,b^a=b^4f,c^a=c^12,d^a=d^12,f^a=f^44228 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16900, 56);