Finite Group DatabasebetaFinite Group Databasebeta| order | 8132 |
| isoclinism | isoclinic class of D107 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic107 |
| unambiguous semidirect product | C107⋊(C4×C19) |
| derived, Sylow | C107 ⋊ C4×C19 |
| Hall | C19×C107 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D107 |
| commutator, hypocenter | C107 | C4×C19 |
| Frattini | C2 | C19×D107 |
| Fitting, socle | C2×C19×C107 | C2 |
| LCS | G ▷ C107 | |
| UCS | C1 ◁ C2×C19 | |
12 conjugacy classes of subgroups.
2090 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C19×Dic107, C19×Dic321, C19⋊C3×Dic107 |
| maximal normal subgroup of | C3×C19×Dic107, C19⋊C3×Dic107 |
| maximal quotient of | C3×C19×Dic107, C19×Dic321 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8132, 3);