Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | D13⋊#89205 |
| derived, Hall | C72×C13 ⋊ C2×C9 |
| Hall | C13⋊#89205 ⋊ C2 |
| Hall | C72×D13 ⋊ C9 |
| Sylow | C72 ⋊ D13⋊C9 |
| Hall | D13 ⋊ #89205 |
| Sylow | C13 ⋊ C2×#89205 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D13⋊#3862 |
| commutator, hypocenter | C72×C13 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C13 | C2×C3 |
| prime radical | C3×C72×D13 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,13,3|b^3=f,e^a=e^12,c^b=c^2,d^b=d^4,e^b=e^3408 conjugacy classes — view the full character table.
| maximal subgroup of | #37524418, D13⋊#11725078, #37524444, … |
| maximal normal subgroup of | #37524418, D13⋊#11725078, #37524444, … |
| maximal quotient of | Dic13⋊#89205, C2×D13⋊#89205 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 117);