Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×C5⋊D5 |
| commutator | C2×C52 | C42 |
| Fitting | C42×C52 | C2 |
| socle, prime radical | C22×C52 | C2×C4 |
| cosocle | C2×C4×C52 | C22 |
| hypercenter | C42 | C5⋊D5 |
| hypocenter | C52 | #97 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,c^2=e,b^a=be,f^a=f^4,g^a=g^4212 conjugacy classes — view the full character table.
| maximal subgroup of | #13099256, #13099258, #13099499, … |
| maximal normal subgroup of | #13099256, #13099258, #13099499, … |
| maximal quotient of | #13099488, #13099498, #13099558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 329);