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 | C23 | D52 |
| commutator | C2×C52 | C42 |
| Fitting, socle, prime radical, cosocle | C23×C52 | C22 |
| hypocenter | C52 | #95 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 | |
206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=c,b^a=be,g^a=g^4,f^b=f^4116 conjugacy classes — view the full character table.
| maximal subgroup of | #13100003, #13100004, #13101232, … |
| maximal normal subgroup of | #13100003, #13100004, #13101232, … |
| maximal quotient of | #13099325, #13099326, #13099327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 279);