Finite Group DatabasebetaFinite Group Databasebeta| order | 14014 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C13 · Schur multiplier (H2) = C7 |
| direct product | C72×C13×D11 |
| unambiguous semidirect product | C11⋊(C2×C72×C13) |
| Fitting, socle, Hall | C72×C11×C13 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C72×C13 |
| Hall | C72×C11 ⋊ C2×C13 |
| Hall | C11×C13 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72×C13 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C72×C13 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11×C13 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C72×C13 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7007 |
4459 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×D11×D13, C7×C13×D7×D11, C7×D11×D91, … |
| maximal normal subgroup of | C72×D11×D13, C7×C13×D7×D11, C7×D11×D91, … |
| maximal quotient of | C72×C13×Dic11, C2×C72×C13×D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14014, 19);