Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D5⋊AGL(1,𝔽5) |
| commutator | C2×C52 | C42 |
| Fitting, socle | C22×C52 | C2×C4 |
| prime radical, cosocle | C22×C5⋊D5 | C22 |
| hypocenter | C52 | #95 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 | |
206 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,b^a=be,f^a=f^3,g^a=g^3,f^b=f^4,f^c=f^4,g^c=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #13103355, #13103356, #13103357, … |
| maximal normal subgroup of | #13103355, #13103356, #13103357, … |
| maximal quotient of | #13099894, #13099895, #13099896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 435);