Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×C5×#713 |
| Fitting | C2×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C22×D5 |
| commutator, cosocle | C2×C5 | C24×C5 |
| Frattini | C2 | C23×C5×D5 |
| Fitting | C2×C52×Q8 | C2 |
| socle | C22×C52 | C23 |
| hypercenter | C2×C5×Q8 | D5 |
| hypocenter | C5 | C2×C5×#41 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C5×Q8 | |
366 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13101719, #13101754, #13101756, … |
| maximal normal subgroup of | #13101719, #13101754, #13101756, … |
| maximal quotient of | C2×C5×#4036, C2×C5×#4038, C2×C5×#4039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1163);