Finite Group DatabasebetaFinite Group Databasebeta| order | 34748 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#19097219 |
| Fitting, socle, derived, Hall | C7×C17×C73 ⋊ C4 |
| Hall | C17×C73 ⋊ Dic7 |
| Hall | C7×C73 ⋊ #595 |
| Hall | C7×C17 ⋊ #64408 |
| Sylow | C73 ⋊ C7⋊#595 |
| Sylow | C17 ⋊ C7⋊#64408 |
| Sylow | C7 ⋊ #19097219 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C17×C73 | C4 |
| prime radical, cosocle | C7×D1241 | C2 |
| LCS | G ▷ C7×C17×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8687 |
Polycyclic presentation:
2^2,7,17,73|a^2=b,c^a=c^6,d^a=d^13,e^a=e^46,d^b=d^16,e^b=e^722180 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34748, 21);