Finite Group DatabasebetaFinite Group Databasebeta| order | 16900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C25×C169 ⋊ C4 |
| Sylow | C169 ⋊ #1035 |
| Sylow | C25 ⋊ Dic169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C169 | C4 |
| Frattini, socle | C5×C13 | #63120 |
| prime radical | C13×D25 | D13 |
| cosocle | D25×C169 | C2 |
| LCS | G ▷ C25×C169 | |
| UCS | C1 | |
27 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4225 |
Polycyclic presentation:
2^2,5,13,5,13|a^2=b,c^5=e^2,d^13=f^12,c^a=c^3e,d^a=d^12f,e^a=e^3,f^a=f^12,c^b=c^4e^3,e^b=e^41186 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16900, 9);