Finite Group DatabasebetaFinite Group Databasebeta| order | 14014 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D1001 |
| unambiguous semidirect product | C11⋊(C7⋊D91) |
| unambiguous semidirect product | C13⋊(C7⋊D77) |
| Fitting, socle, derived, Hall | C72×C11×C13 ⋊ C2 |
| Hall | C72×C13 ⋊ D11 |
| Hall | C72×C11 ⋊ D13 |
| Hall | C11×C13 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D143 |
| Sylow | C13 ⋊ C7⋊D77 |
| Sylow | C11 ⋊ C7⋊D91 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C11×C13 | C2 |
| LCS | G ▷ C72×C11×C13 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7007 |
Polycyclic presentation:
2,7^2,11,13|b^a=b^6,c^a=c^6,d^a=d^10,e^a=e^123505 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D1001, D77×D91, D13×C7⋊D77, … |
| maximal normal subgroup of | D7×D1001, D77×D91, D13×C7⋊D77, … |
| maximal quotient of | C7⋊Dic1001, C2×C7⋊D1001 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14014, 10);