Finite Group DatabasebetaFinite Group Databasebeta| order | 11492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#11725132 |
| Fitting, socle, Hall | C132×C17 ⋊ C4 |
| derived | C13×C17 ⋊ C4×C13 |
| Sylow | C132 ⋊ Dic17 |
| Sylow | C17 ⋊ C13×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #11725132 |
| commutator, hypocenter | C13×C17 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C132×C17 | C4 |
| prime radical | C13×C17×D13 | C2 |
| cosocle | C17×D13 | C2×C13 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 ◁ C13 | |
30 conjugacy classes of subgroups.
923 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#11725132⋊C3, C13⋊C3×#11725132, #46828265, … |
| maximal normal subgroup of | C13×#11725132⋊C3, C13⋊C3×#11725132, #46828265, … |
| maximal quotient of | C3×C13×#11725132, C13×C3⋊#11725132 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11492, 27);