Finite Group DatabasebetaFinite Group Databasebeta| order | 820 |
| isoclinism | isoclinic class of #11717962 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C41 ⋊ C4 |
| Sylow | C41 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C41 | C4 |
| prime radical, cosocle | D205 | C2 |
| LCS | G ▷ C5×C41 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 205 |
Polycyclic presentation:
2^2,5,41|a^2=b,c^a=c^3,d^a=d^32,c^b=c^4,d^b=d^4055 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#4223, C2×#11717962, C3×#11717962, … |
| maximal normal subgroup of | D5⋊#4223, C2×#11717962, C3×#11717962, … |
| maximal quotient of | #13109983, C2×#11717962, C3×#11717962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(820, 13);