Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#16838480 |
| Fitting, socle | C3×C72×C13 ⋊ C2×C3 |
| derived, Hall | C72×C13 ⋊ C2×C32 |
| Hall | C3×C7×#63271 ⋊ C2 |
| Hall | C7×D91 ⋊ C32 |
| Sylow | C72 ⋊ C3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16838480 |
| commutator, cosocle, hypocenter | C72×C13 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C2×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
100 conjugacy classes of subgroups.
369 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10587721⋊D7, C3×#10587723⋊D7, C3×D7×#10587717, … |
| maximal normal subgroup of | C3×#10587721⋊D7, C3×#10587723⋊D7, C3×D7×#10587717, … |
| maximal quotient of | C3×#21439556, C2×C3×#16838480 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 266);