Finite Group DatabasebetaFinite Group Databasebeta| order | 12388 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic163 |
| unambiguous semidirect product | C163⋊(C4×C19) |
| derived, Sylow | C163 ⋊ C4×C19 |
| Hall | C19×C163 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D163 |
| commutator, hypocenter | C163 | C4×C19 |
| Frattini | C2 | C19×D163 |
| Fitting, socle, prime radical | C2×C19×C163 | C2 |
| cosocle | C2×C163 | C2×C19 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C2×C19 | |
12 conjugacy classes of subgroups.
3154 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C19×Dic163, C19×Dic489, C19×(C163⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C19×Dic163, C19×(C163⋊C3)⋊C4, C19⋊C3×Dic163, … |
| maximal quotient of | C3×C19×Dic163, C19×Dic489 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12388, 3);