Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting | C52×C16 ⋊ C2 |
| Sylow | C52 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×C5⋊D5 |
| commutator, socle | C2×C52 | C2×C8 |
| Fitting | C52×C16 | C2 |
| prime radical | C2×C5⋊D5 | C8 |
| cosocle | C52×C8 | C22 |
| hypercenter | C16 | C5⋊D5 |
| hypocenter | C52 | M32 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C8 ◁ C16 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=c,c^2=d,d^2=e,b^a=be,f^a=f^4,g^a=g^4212 conjugacy classes — view the full character table.
| maximal subgroup of | #13100223, #13100224, #13100225, … |
| maximal normal subgroup of | #13100223, #13100224, #13100225, … |
| maximal quotient of | #13099535, #13099536, #13099540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 324);