Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C25 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D25 |
| commutator | C2×C25 | C42 |
| Frattini, socle, prime radical | C23×C5 | C2×D5 |
| Fitting | C22×C4×C25 | C2 |
| cosocle | C23×C25 | C22 |
| hypercenter | C22×C4 | D25 |
| hypocenter | C25 | #95 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,f^5=g,b^a=be,f^a=f^4g^4,g^a=g^4212 conjugacy classes — view the full character table.
| maximal subgroup of | #13097674, #13097676, #13097743, … |
| maximal normal subgroup of | #13097674, #13097676, #13097743, … |
| maximal quotient of | #13097729, #13097730, #13097732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 38);