Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C2×C3×C13⋊#3862 |
| unambiguous semidirect product | (C2×C3×C13)⋊#3862 |
| Fitting, socle | C2×C3×C72×C13 ⋊ C3 |
| derived, Hall | C72×C13 ⋊ C2×C32 |
| Hall | C2×C72×C13 ⋊ C32 |
| Hall | C2×C72 ⋊ C3×C13⋊C3 |
| Sylow | C72 ⋊ C2×C3×C13⋊C3 |
| Hall | C2×C13 ⋊ C3×#3862 |
| Sylow | C13 ⋊ C2×C3×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C13⋊#3862 |
| commutator, cosocle, hypocenter | C72×C13 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C72×C13 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C2×C3 | |
112 conjugacy classes of subgroups.
1290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#21439528, C3×#21439529, C3×#21439538, … |
| maximal normal subgroup of | C3×#21439528, C3×#21439529, C3×#21439538, … |
| maximal quotient of | C3×C4×C13⋊#3862, C22×C3×C13⋊#3862 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 339);