Finite Group DatabasebetaFinite Group Databasebeta| order | 10820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14524194⋊C5 |
| Fitting, socle, derived, Sylow | C541 ⋊ C4×C5 |
| Hall | C541⋊C5 ⋊ C4 |
| Hall | #14524194 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C541 | C4×C5 |
| prime radical | D541⋊C5 | C2 |
| cosocle | D541 | C2×C5 |
| LCS | G ▷ C541 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,541|a^2=c,d^a=d^489,d^b=d^48,d^c=d^54047 conjugacy classes — view the full character table.
| maximal subgroup of | (#14524194⋊C3)⋊C5, C3×#14524194⋊C5, C3⋊(#14524194⋊C5) |
| maximal normal subgroup of | (#14524194⋊C3)⋊C5, C3×#14524194⋊C5 |
| maximal quotient of | C3×#14524194⋊C5, C3⋊(#14524194⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10820, 8);