Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C72×C13 ⋊ C3×D3 |
| derived | C13×#3862 ⋊ C2×C3 |
| Hall | #19153211 ⋊ C2 |
| Sylow | C72 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ #64418⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C13×#3862 | C2×C3 |
| Fitting, socle | C72×C13 | C3×D3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,13,7^2|c^a=c^2,d^a=d^12,e^a=e^2f^3,f^a=e^6f^5,d^b=d^3,e^b=e^4,f^b=f^4,e^c=e^4f^4,f^c=f^258 conjugacy classes — view the full character table.
| maximal subgroup of | #37524843, #37524845, #37524861, … |
| maximal normal subgroup of | #37524843, #37524845, #37524861, … |
| maximal quotient of | #37524679, C2×#26039561 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 204);