Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#6014 |
| derived, Sylow | C25 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D25 |
| commutator, hypocenter | C25 | C22×C8 |
| Frattini | C4×C5 | C22×D5 |
| Fitting | C22×C4×C25 | C2 |
| socle, prime radical | C23×C5 | Dic5 |
| cosocle | C4×C25 | C23 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C22×C4 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #13097729, #13097736, #13097757, … |
| maximal normal subgroup of | #13097729, #13097736, #13097757, … |
| maximal quotient of | C2×C4×#6014, C2×C4⋊#6014, #13098200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 141);