Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊Dic37 |
| unambiguous semidirect product | Dic407⋊C5 |
| derived, Hall | C11×C37 ⋊ C4×C5 |
| Hall | C37×C11⋊C5 ⋊ C4 |
| Hall | Dic407 ⋊ C5 |
| Hall | C11⋊C5 ⋊ Dic37 |
| Sylow | C37 ⋊ Dic11⋊C5 |
| Sylow | C11 ⋊ C5×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C37⋊AGL(1,𝔽11) |
| commutator, hypocenter | C11×C37 | C4×C5 |
| Fitting, socle | C2×C11×C37 | C2×C5 |
| LCS | G ▷ C11×C37 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,37,2|a^2=e,c^a=c^10,d^a=d^36,c^b=c^4274 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C11⋊C5)⋊Dic37, C3⋊((C11⋊C5)⋊Dic37), (C11⋊C5)⋊(Dic37⋊C3) |
| maximal normal subgroup of | C3×(C11⋊C5)⋊Dic37, (C11⋊C5)⋊(Dic37⋊C3) |
| maximal quotient of | C3×(C11⋊C5)⋊Dic37, C3⋊((C11⋊C5)⋊Dic37) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 12);