Finite Group DatabasebetaFinite Group Databasebeta| order | 5842 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C127 · Schur multiplier (H2) = C1 |
| direct product | D23×C127 |
| unambiguous semidirect product | C23⋊(C2×C127) |
| Fitting, socle, Hall | C23×C127 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C127 | D23 |
| commutator, hypocenter | C23 | C2×C127 |
| Frattini | C1 | G |
| Fitting, socle | C23×C127 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C127 | |
8 conjugacy classes of subgroups.
1651 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D127, C2×D23×C127, C3×D23×C127, … |
| maximal normal subgroup of | D23×D127, C2×D23×C127, C3×D23×C127, … |
| maximal quotient of | Dic23×C127, C2×D23×C127, C3×D23×C127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5842, 1);