Finite Group DatabasebetaFinite Group Databasebeta| order | 5410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D541⋊C5 |
| unambiguous semidirect product | (C541⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C541 ⋊ C2×C5 |
| Hall | C541⋊C5 ⋊ C2 |
| Hall | D541 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C541 | C2×C5 |
| LCS | G ▷ C541 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,541|c^a=c^540,c^b=c^4864 conjugacy classes — view the full character table.
| maximal subgroup of | #14524194⋊C5, C2×D541⋊C5, C3×D541⋊C5, … |
| maximal normal subgroup of | #14524194⋊C5, C2×D541⋊C5, C3×D541⋊C5, … |
| maximal quotient of | Dic541⋊C5, C2×D541⋊C5, C3×D541⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5410, 1);