Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C52 ⋊ #108 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^3,g^a=g^3,f^b=f^4,f^c=f^4,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#3995, #13103868, D5⋊#3996, … |
| maximal normal subgroup of | D5⋊#3995, #13103868, D5⋊#3996, … |
| maximal quotient of | #13099892, #13099893, #13099911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 432);