Finite Group DatabasebetaFinite Group Databasebeta| order | 17980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D145⋊D31 |
| unambiguous semidirect product | D155⋊D29 |
| unambiguous semidirect product | D899⋊D5 |
| Fitting, socle, derived, Hall | C5×C29×C31 ⋊ C22 |
| Hall | C29×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D29 |
| Hall | C5×C29 ⋊ C2×D31 |
| Sylow | C31 ⋊ D5×D29 |
| Sylow | C29 ⋊ D5×D31 |
| Sylow | C5 ⋊ D29×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C29×C31 | C22 |
| LCS | G ▷ C5×C29×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4495 |
Polycyclic presentation:
2^2,5,29,31|d^a=d^28,e^a=e^30,c^b=c^4,d^b=d^281174 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17980, 39);