Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C52 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#6053 |
| commutator, socle | C2×C52 | C2×C8 |
| Fitting | C4×C52 | C8 |
| prime radical | C2×C5⋊D5 | C8 |
| cosocle | #6033 | C22 |
| hypercenter | C4 | #6053 |
| hypocenter | C52 | M32 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C4 | |
59 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=e,c^2=d,d^2=e,b^a=be,f^a=g,g^a=f^2,f^c=f^2,g^c=g^2,f^d=f^4,g^d=g^432 conjugacy classes — view the full character table.
| maximal subgroup of | #13103296, #13103298, #13103402, … |
| maximal normal subgroup of | #13103296, #13103298, #13103402, … |
| maximal quotient of | #13103408, #13103409, C4⋊#87822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 975);