Finite Group DatabasebetaFinite Group Databasebeta| order | 11822 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C257 · Schur multiplier (H2) = C1 |
| direct product | D23×C257 |
| unambiguous semidirect product | C23⋊(C2×C257) |
| Fitting, socle, Hall | C23×C257 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C257 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C257 | D23 |
| commutator, cosocle, hypocenter | C23 | C2×C257 |
| Frattini | C1 | G |
| Fitting, socle | C23×C257 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C257 | |
8 conjugacy classes of subgroups.
3341 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D257, C2×D23×C257, C3×D23×C257, … |
| maximal normal subgroup of | D23×D257, C2×D23×C257, C3×D23×C257 |
| maximal quotient of | Dic23×C257, C2×D23×C257, C3×D23×C257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11822, 1);