Finite Group DatabasebetaFinite Group Databasebeta| order | 5405 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C5×C47⋊C23 |
| unambiguous semidirect product | C47⋊(C5×C23) |
| unambiguous semidirect product | (C5×C47)⋊C23 |
| Fitting, socle, Hall | C5×C47 ⋊ C23 |
| derived, Sylow | C47 ⋊ C5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C47⋊C23 |
| commutator, hypocenter | C47 | C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C47 | C23 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
125 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×C47⋊C23, C5×AGL(1,𝔽47), D5×C47⋊C23, … |
| maximal normal subgroup of | C2×C5×C47⋊C23, C5×AGL(1,𝔽47), D5×C47⋊C23, … |
| maximal quotient of | C2×C5×C47⋊C23, C3×C5×C47⋊C23, C25×C47⋊C23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5405, 1);