Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×C5⋊D5 |
| commutator | C2×C52 | C42 |
| Fitting | C22×C4×C52 | C2 |
| socle, prime radical, cosocle | C23×C52 | C22 |
| hypercenter | C22×C4 | C5⋊D5 |
| hypocenter | C52 | #95 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
304 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,b^a=be,f^a=f^4,g^a=g^4212 conjugacy classes — view the full character table.
| maximal subgroup of | #13099320, #13099322, #13099503, … |
| maximal normal subgroup of | #13099320, #13099322, #13099503, … |
| maximal quotient of | #13099557, #13099558, #13099560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 357);