Finite Group DatabasebetaFinite Group Databasebeta| order | 16214 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×D67 |
| Fitting, socle, Hall | C112×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | D67 |
| commutator, cosocle, hypocenter | C67 | C2×C112 |
| Frattini | C1 | G |
| Fitting, socle | C112×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C112 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8107 |
4235 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D67, D67×C11⋊D11, C2×C112×D67 |
| maximal normal subgroup of | C11×D11×D67, D67×C11⋊D11, C2×C112×D67 |
| maximal quotient of | C112×Dic67, C2×C112×D67 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16214, 16);