Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #6053⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #6053⋊C4 |
| Sylow | C52 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #6053⋊C2 |
| commutator | C5⋊D5 | C42 |
| Fitting, socle | C2×C52 | M16 |
| prime radical | C2×C5⋊D5 | C2×C4 |
| cosocle | C2×#1043 | C22 |
| hypocenter | C52 | #97 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C2 | |
63 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=de,b^2=c,c^2=e,b^a=be,f^a=f^2,g^a=g^3,f^b=g,g^b=f^2,f^c=f^2,g^c=g^2,f^e=f^4,g^e=g^426 conjugacy classes — view the full character table.
| maximal subgroup of | #13107441, #13107442, #6053⋊Q8, … |
| maximal normal subgroup of | #13107441, #13107442, #6053⋊Q8, … |
| maximal quotient of | #6053⋊C8, #13103296, #13103302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 962);