Finite Group DatabasebetaFinite Group Databasebeta| order | 17270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊D157 |
| unambiguous semidirect product | C157⋊AGL(1,𝔽11) |
| unambiguous semidirect product | D1727⋊C5 |
| Fitting, socle, derived, Hall | C11×C157 ⋊ C2×C5 |
| Hall | C11⋊C5×C157 ⋊ C2 |
| Hall | D1727 ⋊ C5 |
| Sylow | C157 ⋊ AGL(1,𝔽11) |
| Hall | C11⋊C5 ⋊ D157 |
| Sylow | C11 ⋊ C5×D157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C157 | C2×C5 |
| LCS | G ▷ C11×C157 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1727 |
Polycyclic presentation:
2,5,11,157|c^a=c^10,d^a=d^156,c^b=c^4557 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×D157, C2×(C11⋊C5)⋊D157 |
| maximal normal subgroup of | AGL(1,𝔽11)×D157, C2×(C11⋊C5)⋊D157 |
| maximal quotient of | (C11⋊C5)⋊Dic157, C2×(C11⋊C5)⋊D157 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17270, 12);