Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4×C5 |
| direct product | C8×#1039 |
| derived, Sylow | C52 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | C5⋊D5 |
| commutator, hypocenter | C52 | C4×C8 |
| Frattini | C2×C4 | C2×C5⋊D5 |
| Fitting | C2×C52×C8 | C2 |
| socle, prime radical | C22×C52 | C2×C4 |
| cosocle | C2×C4×C52 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C8 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #13099272, #13099274, #13099303, … |
| maximal normal subgroup of | #13099272, #13099274, #13099303, … |
| maximal quotient of | C8×#6029, #13099488, C16×#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 339);