Finite Group DatabasebetaFinite Group Databasebeta| order | 11210 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C59 · Schur multiplier (H2) = C1 |
| direct product | C5×D19×C59 |
| unambiguous semidirect product | C19⋊(C2×C5×C59) |
| Fitting, socle, Hall | C5×C19×C59 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C5×C59 |
| Hall | C19×C59 ⋊ C2×C5 |
| Hall | C5×C19 ⋊ C2×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C59 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C5×C59 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C59 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C5×C59 | |
16 conjugacy classes of subgroups.
3245 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D19×D59, D5×D19×C59, D19×D295, … |
| maximal normal subgroup of | C5×D19×D59, D5×D19×C59, D19×D295, … |
| maximal quotient of | C5×C59×Dic19, C2×C5×D19×C59, C3×C5×D19×C59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11210, 3);