Finite Group DatabasebetaFinite Group Databasebeta| order | 5428 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic59 |
| unambiguous semidirect product | C59⋊(C4×C23) |
| derived, Sylow | C59 ⋊ C4×C23 |
| Hall | C23×C59 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D59 |
| commutator, hypocenter | C59 | C4×C23 |
| Frattini | C2 | C23×D59 |
| Fitting, socle | C2×C23×C59 | C2 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C23 | |
12 conjugacy classes of subgroups.
1426 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C23×Dic59, C23×Dic177, C5×C23×Dic59, … |
| maximal normal subgroup of | C3×C23×Dic59, C5×C23×Dic59, C7×C23×Dic59 |
| maximal quotient of | C3×C23×Dic59, C23×Dic177, C5×C23×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5428, 3);