Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #106 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #6038 |
| commutator | C4×C52 | C2×C4 |
| Frattini, hypercenter | C2×C4 | D52 |
| Fitting, cosocle | C2×C4×C52 | C22 |
| socle, prime radical | C22×C52 | D4 |
| hypocenter | C52 | #106 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=c,c^2=e,b^a=bc,c^a=ce,g^a=g^4,f^b=f^498 conjugacy classes — view the full character table.
| maximal subgroup of | #13100448, #13100449, #13100464, … |
| maximal normal subgroup of | #13100448, #13100449, #13100464, … |
| maximal quotient of | #13099267, #13099306, #13099307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 273);