Finite Group DatabasebetaFinite Group Databasebeta| order | 17020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D115⋊D37 |
| unambiguous semidirect product | D185⋊D23 |
| unambiguous semidirect product | D851⋊D5 |
| Fitting, socle, derived, Hall | C5×C23×C37 ⋊ C22 |
| Hall | C23×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×D23 |
| Hall | C5×C23 ⋊ C2×D37 |
| Sylow | C37 ⋊ D5×D23 |
| Sylow | C23 ⋊ D5×D37 |
| Sylow | C5 ⋊ D23×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C23×C37 | C22 |
| LCS | G ▷ C5×C23×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4255 |
Polycyclic presentation:
2^2,5,23,37|d^a=d^22,e^a=e^36,c^b=c^4,d^b=d^221114 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17020, 28);