Finite Group DatabasebetaFinite Group Databasebeta| order | 11001 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C193 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×C193 |
| unambiguous semidirect product | C19⋊(C3×C193) |
| Fitting, socle, Hall | C19×C193 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C193 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C193 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C3×C193 |
| Frattini | C1 | G |
| Fitting, socle | C19×C193 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C193 | |
8 conjugacy classes of subgroups.
1737 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19⋊C3×C193, C19⋊C3×D193, D19⋊C3×C193, … |
| maximal normal subgroup of | C2×C19⋊C3×C193, C19⋊C3×D193, D19⋊C3×C193, … |
| maximal quotient of | C2×C19⋊C3×C193, #4294×C193, C3×C19⋊C3×C193 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11001, 1);