Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#10625193 |
| Fitting, socle, derived, Hall | C5×C11×C37 ⋊ C4 |
| Hall | C11×C37 ⋊ AGL(1,𝔽5) |
| Hall | C5×C37 ⋊ Dic11 |
| Hall | C5×C11 ⋊ Dic37 |
| Sylow | C37 ⋊ C11⋊AGL(1,𝔽5) |
| Sylow | C11 ⋊ #10625193 |
| Sylow | C5 ⋊ Dic407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C37 | C4 |
| LCS | G ▷ C5×C11×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,11,37|a^2=b,c^a=c^2,d^a=d^10,e^a=e^36,c^b=c^4817 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊(#10625193⋊C3), C3×C11⋊#10625193, C3⋊(C11⋊#10625193) |
| maximal normal subgroup of | C11⋊(#10625193⋊C3), C3×C11⋊#10625193 |
| maximal quotient of | C3×C11⋊#10625193, C3⋊(C11⋊#10625193) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 31);