Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #1044 |
| commutator, hypocenter | C52 | C32 |
| Fitting | C52×C8 | C4 |
| socle, prime radical | C2×C52 | C16 |
| cosocle | #87756 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C8 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^5,5^2|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^3,g^a=g^2,f^b=f^4,g^b=g^480 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#3928, #13099873, #13099956, … |
| maximal normal subgroup of | D5⋊#3928, #13099873, #13099956, … |
| maximal quotient of | #13099235, C2×#11716581 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 240);