Finite Group DatabasebetaFinite Group Databasebeta| order | 16214 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C67 · Schur multiplier (H2) = C1 |
| direct product | C11×D11×C67 |
| unambiguous semidirect product | C11⋊(C2×C11×C67) |
| Fitting, socle, Hall | C112×C67 ⋊ C2 |
| derived | C11 ⋊ C2×C11×C67 |
| Sylow | C112 ⋊ C2×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C67 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C11×C67 |
| Frattini | C1 | G |
| Fitting, socle | C112×C67 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C11×C67 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1474 |
5159 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D67, D112×C67, D11×D737, … |
| maximal normal subgroup of | C11×D11×D67, D112×C67, D11×D737, … |
| maximal quotient of | C11×Dic11×C67, C2×C11×D11×C67 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16214, 15);