Finite Group DatabasebetaFinite Group Databasebeta| order | 34340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D85⋊D101 |
| unambiguous semidirect product | D505⋊D17 |
| unambiguous semidirect product | D1717⋊D5 |
| Fitting, socle, derived, Hall | C5×C17×C101 ⋊ C22 |
| Hall | C17×C101 ⋊ C2×D5 |
| Hall | C5×C101 ⋊ C2×D17 |
| Sylow | C101 ⋊ D5×D17 |
| Hall | C5×C17 ⋊ C2×D101 |
| Sylow | C17 ⋊ D5×D101 |
| Sylow | C5 ⋊ D17×D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C17×C101 | C22 |
| LCS | G ▷ C5×C17×C101 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8585 |
Polycyclic presentation:
2^2,5,17,101|d^a=d^16,e^a=e^100,c^b=c^4,d^b=d^162240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34340, 59);