Finite Group DatabasebetaFinite Group Databasebeta| order | 5428 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D59 |
| unambiguous semidirect product | (D23×C59)⋊C2 |
| unambiguous semidirect product | (C23×D59)⋊C2 |
| unambiguous semidirect product | D1357⋊C2 |
| Fitting, socle, derived, Hall | C23×C59 ⋊ C22 |
| Sylow | C59 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C59 | C22 |
| LCS | G ▷ C23×C59 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
403 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D23×D59, D59×D69, D23×D177, … |
| maximal normal subgroup of | C3×D23×D59, C5×D23×D59, C7×D23×D59 |
| maximal quotient of | C3×D23×D59, D59×D69, D23×D177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5428, 6);