Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D52⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#87836 |
| Sylow | C52 ⋊ C2×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D52⋊C2 |
| commutator | C5⋊D5 | C22×C4 |
| Frattini | C2 | C2×D52⋊C2 |
| Fitting, socle | C22×C52 | D4 |
| 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 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | #13103354, #13103355, #13103357, … |
| maximal normal subgroup of | #13103354, #13103355, #13103357, … |
| maximal quotient of | #13104172, C2×#11716790, #13104224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1051);