Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×#1043 |
| Fitting | C52×D4 ⋊ C4 |
| Sylow | C52 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#1043 |
| commutator, socle | C2×C52 | C22×C4 |
| Fitting | C52×D4 | C4 |
| prime radical | D4×C5⋊D5 | C2 |
| cosocle | C2×C5⋊D5 | C23 |
| hypercenter | D4 | #1043 |
| hypocenter | C52 | C4×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ D4 | |
376 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#6053, #13104055, #13104056, … |
| maximal normal subgroup of | D4⋊#6053, #13104055, #13104056, … |
| maximal quotient of | #13104704, #13104705, #13104706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1099);