Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4×C5 |
| direct product | C42×C5⋊D5 |
| Fitting | C42×C52 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C42 |
| Frattini | C22 | C22×C5⋊D5 |
| Fitting | C42×C52 | C2 |
| socle, cosocle | C22×C52 | C23 |
| prime radical | C22×C5⋊D5 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C42 | |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #13100240, #13100332, #13100434, … |
| maximal normal subgroup of | #13100240, #13100332, #13100434, … |
| maximal quotient of | #13102509, #13102512, #13102513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 850);