Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #6057 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×#87840 |
| Sylow | C52 ⋊ C2×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #6057 |
| commutator | C5⋊D5 | C22×C4 |
| Frattini | C2 | C2×#6057 |
| Fitting, socle | C22×C52 | Q8 |
| prime radical | C22×C5⋊D5 | C22 |
| cosocle | C2×C5⋊D5 | C23 |
| hypocenter | C52 | C2×C4⋊C4 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C22 | |
173 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
32 conjugacy classes — view the full character table.
| maximal subgroup of | #13103354, #13103355, #13103357, … |
| maximal normal subgroup of | #13103354, #13103355, #13103357, … |
| maximal quotient of | #13104401, C2×#11716802, #13104403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1063);