Finite Group DatabasebetaFinite Group Databasebeta| order | 10868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C19⋊#261) |
| unambiguous semidirect product | C19⋊(C11⋊#261) |
| Fitting, socle, derived, Hall | C11×C13×C19 ⋊ C4 |
| Hall | C13×C19 ⋊ Dic11 |
| Hall | C11×C19 ⋊ #261 |
| Hall | C11×C13 ⋊ Dic19 |
| Sylow | C19 ⋊ C11⋊#261 |
| Sylow | C13 ⋊ Dic209 |
| Sylow | C11 ⋊ C19⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C13×C19 | C4 |
| prime radical, cosocle | C11×C19×D13 | C2 |
| LCS | G ▷ C11×C13×C19 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,11,13,19|a^2=b,c^a=c^10,d^a=d^5,e^a=e^18,d^b=d^12839 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊#15688300, C11⋊#15688301, C11⋊#15688304, … |
| maximal normal subgroup of | C11⋊#15688300, C11⋊#15688301, C11⋊#15688304, … |
| maximal quotient of | C3×C11⋊(C19⋊#261), C3⋊(C11⋊(C19⋊#261)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10868, 15);