Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#1042 |
| Fitting | C2×C4×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #1042 |
| commutator, hypocenter | C52 | C2×C42 |
| Frattini | C2 | C22×#1042 |
| Fitting | C2×C4×C52 | C4 |
| socle | C22×C52 | C2×C4 |
| prime radical | C22×C5×D5 | C22 |
| cosocle | C2×C5×D5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #13099779, #13099784, #13099787, … |
| maximal normal subgroup of | #13099779, #13099784, #13099787, … |
| maximal quotient of | C4×D5⋊#168, #13104562, C4×#87849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1082);