Finite Group DatabasebetaFinite Group Databasebeta| order | 28900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C52×C289 ⋊ C4 |
| Sylow | C289 ⋊ #1042 |
| Sylow | C52 ⋊ Dic289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C289 | C4 |
| Frattini | C17 | #13133352 |
| socle | C52×C17 | Dic17 |
| prime radical | C5×D5×C17 | D17 |
| cosocle | C5×D5×C289 | C2 |
| LCS | G ▷ C52×C289 | |
| UCS | C1 | |
39 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5780 |
Polycyclic presentation:
2^2,5^2,17^2|a^2=b,e^17=f^16,c^a=c^2,d^a=d^4,e^a=e^16f,f^a=f^16,c^b=c^42893 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28900, 39);