Finite Group DatabasebetaFinite Group Databasebeta| order | 30260 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C17×C89 ⋊ C4 |
| Hall | C17×C89 ⋊ AGL(1,𝔽5) |
| Hall | C5×C89 ⋊ Dic17 |
| Sylow | C89 ⋊ #66774 |
| Hall | C5×C17 ⋊ Dic89 |
| Sylow | C17 ⋊ #13184069 |
| Sylow | C5 ⋊ Dic1513 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17×C89 | C4 |
| prime radical, cosocle | D5×C17×C89 | C2 |
| LCS | G ▷ C5×C17×C89 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7565 |
Polycyclic presentation:
2^2,5,17,89|a^2=b,c^a=c^2,d^a=d^16,e^a=e^88,c^b=c^43029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30260, 32);