Finite Group DatabasebetaFinite Group Databasebeta| order | 11349 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×C13⋊C9 |
| unambiguous semidirect product | C13⋊(C9×C97) |
| derived, Sylow | C13 ⋊ C9×C97 |
| Hall | C13×C97 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C97 | C13⋊C3 |
| commutator, hypocenter | C13 | C9×C97 |
| Frattini | C3 | C13⋊C3×C97 |
| Fitting, socle, prime radical | C3×C13×C97 | C3 |
| cosocle | C3×C13 | C3×C97 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C97 | |
12 conjugacy classes of subgroups.
2037 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C97×C13⋊C9, C13⋊C9×D97, C97×D13⋊C9, … |
| maximal normal subgroup of | C2×C97×C13⋊C9, C13⋊C9×D97, C97×D13⋊C9, … |
| maximal quotient of | C2×C97×C13⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11349, 2);