Finite Group DatabasebetaFinite Group Databasebeta| order | 17157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#11744749 |
| Fitting, socle, Hall | C7×C19×C43 ⋊ C3 |
| derived, Hall | C7×C43 ⋊ C3×C19 |
| Hall | C19×C43 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C19 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ C19×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C19×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #11744749 |
| commutator, cosocle, hypocenter | C7×C43 | C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C43 | C3 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5719 |
1957 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19×#11744749, C19×#14268588, D19×#11744749, … |
| maximal normal subgroup of | C2×C19×#11744749, C19×#14268588, D19×#11744749, … |
| maximal quotient of | C2×C19×#11744749 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17157, 8);