Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Sylow | C52 ⋊ Q32 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^4,g^a=g^4,c^b=cd,d^b=de95 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3961, #13101223, #13101226, … |
| maximal normal subgroup of | D5×#3961, #13101223, #13101226, … |
| maximal quotient of | #13099523, #13099526, #13099598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 355);