Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #6057 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Sylow | C52 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #6057 |
| commutator | C5⋊D5 | C2×C8 |
| Fitting | C4×C52 | Q8 |
| socle | C2×C52 | C4⋊C4 |
| prime radical | C2×C5⋊D5 | C2×C4 |
| cosocle | C4×C5⋊D5 | C22 |
| hypocenter | C52 | C4⋊C8 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C4 | |
75 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=cd,d^2=e,b^a=bc,f^a=f^2,g^a=g^3,f^b=g,g^b=f^4,f^c=f^4,g^c=g^432 conjugacy classes — view the full character table.
| maximal subgroup of | #13103306, #13103307, #13103308, … |
| maximal normal subgroup of | #13103306, #13103307, #13103308, … |
| maximal quotient of | #13100014, #13100015, #13100020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 461);