Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C13 ⋊ C2×C9 |
| Hall | C7×#11717941 ⋊ C2 |
| Hall | C13×C7⋊D7 ⋊ C9 |
| Hall | C7⋊D7 ⋊ C13⋊C9 |
| Sylow | C72 ⋊ C2×C13⋊C9 |
| Sylow | C13 ⋊ (C7⋊C9)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16838470 |
| commutator, hypocenter | C72×C13 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C13 | C2×C3 |
| prime radical | C3×C13×C7⋊D7 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,13,3|b^3=f,c^a=c^6,d^a=d^6,c^b=c^2,e^b=e^3378 conjugacy classes — view the full character table.
| maximal subgroup of | #13109902⋊D7, D7×#13109900, #13109896⋊D7, … |
| maximal normal subgroup of | #13109902⋊D7, D7×#13109900, #13109896⋊D7, … |
| maximal quotient of | #37524361, C2×#26039468 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 111);