Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D52 |
| commutator, socle | C2×C52 | C22×C4 |
| Fitting | C52×C8 | C22 |
| prime radical | #87873 | C2 |
| cosocle | C4×C52 | C23 |
| hypercenter | C8 | D52 |
| hypocenter | C52 | #131 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C8 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|c^2=d,d^2=e,b^a=be,c^a=ce,g^a=g^4,c^b=ce,f^b=f^492 conjugacy classes — view the full character table.
| maximal subgroup of | #13099946, #13103837, #13103839, … |
| maximal normal subgroup of | #13099946, #13103837, #13103839, … |
| maximal quotient of | #13100859, #13100861, #13100862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 582);