Finite Group DatabasebetaFinite Group Databasebeta| order | 17157 |
| isoclinism | isoclinic class of #87704 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×#87704 |
| Fitting, socle, Hall | C7×C19×C43 ⋊ C3 |
| derived, Hall | C7×C19 ⋊ C3×C43 |
| Hall | C19×C43 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C43 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×C43 |
| Sylow | C7 ⋊ C43×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #87704 |
| commutator, cosocle, hypocenter | C7×C19 | C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C43 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5719 |
2021 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C43×#87704, D43×#87704, C43×#11716321, … |
| maximal normal subgroup of | C2×C43×#87704, D43×#87704, C43×#11716321, … |
| maximal quotient of | C2×C43×#87704 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17157, 10);