Finite Group DatabasebetaFinite Group Databasebeta| order | 17157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C19×C43 ⋊ C3 |
| Hall | C19×C43 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C43 ⋊ C19⋊C3 |
| Hall | C7×C19 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ #87705 |
| Sylow | C19 ⋊ #11744748 |
| Sylow | C7 ⋊ #14578576 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C19×C43 | C3 |
| LCS | G ▷ C7×C19×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5719 |
Polycyclic presentation:
3,7,19,43|b^a=b^2,c^a=c^11,d^a=d^61909 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#31769767, #46804922, #46804935, … |
| maximal normal subgroup of | C2×#31769767, #46804922, #46804935, … |
| maximal quotient of | C2×#31769767 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17157, 15);