Finite Group DatabasebetaFinite Group Databasebeta| order | 5410 |
| automorphism | Aut(G) order 5842800 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2705 |
| unambiguous semidirect product | C5⋊D541 |
| unambiguous semidirect product | C541⋊D5 |
| Fitting, socle, derived, Hall | C5×C541 ⋊ C2 |
| Sylow | C541 ⋊ D5 |
| Sylow | C5 ⋊ D541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C541 | C2 |
| LCS | G ▷ C5×C541 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,541|b^a=b^4,c^a=c^5401354 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24925266, #24925267, D5×D541, … |
| maximal normal subgroup of | #24925266, #24925267, D5×D541, … |
| maximal quotient of | Dic2705, C2×D2705, C3×D2705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5410, 5);