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 ⋊ #1043 |
| Sylow | C52 ⋊ #11923876 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C289 | C4 |
| Frattini | C17 | #13133343 |
| socle | C52×C17 | #595 |
| prime radical, cosocle | C5⋊D1445 | C2 |
| LCS | G ▷ C52×C289 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7225 |
Polycyclic presentation:
2^2,5^2,17^2|a^2=b,e^17=f^11,c^a=c^2,d^a=d^2,e^a=e^13f,f^a=f^13,c^b=c^4,d^b=d^4,e^b=e^16f^6,f^b=f^161810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28900, 30);