Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C42×D25 |
| Fitting | C42×C25 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D25 |
| commutator, hypocenter | C25 | C2×C42 |
| Frattini, socle | C22×C5 | C22×D5 |
| Fitting | C42×C25 | C2 |
| prime radical | C22×D25 | C22 |
| cosocle | C22×C25 | C23 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C42 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #13097848, C4×C8×D25, #13097962, … |
| maximal normal subgroup of | #13097848, C4×C8×D25, #13097962, … |
| maximal quotient of | #13097921, #13097924, #13097925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 92);