Finite Group DatabasebetaFinite Group Databasebeta| order | 11342 |
| isoclinism | isoclinic class of D107 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D107 |
| Fitting, socle, Hall | C53×C107 ⋊ C2 |
| derived, Sylow | C107 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D107 |
| commutator, cosocle, hypocenter | C107 | C2×C53 |
| Frattini | C1 | G |
| Fitting, socle | C53×C107 | C2 |
| LCS | G ▷ C107 | |
| UCS | C1 ◁ C53 | |
8 conjugacy classes of subgroups.
2915 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×D107, C2×C53×D107, C3×C53×D107, … |
| maximal normal subgroup of | D53×D107, C2×C53×D107, C3×C53×D107 |
| maximal quotient of | C53×Dic107, C2×C53×D107, C3×C53×D107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11342, 4);