Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
| direct product | C2×#87904 |
| Fitting | C2×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C5⋊D5 |
| commutator, cosocle | C2×C52 | C24 |
| Frattini | C2 | C23×C5⋊D5 |
| Fitting | C2×C52×Q8 | C2 |
| socle | C22×C52 | C23 |
| hypercenter | C2×Q8 | C5⋊D5 |
| hypocenter | C52 | C2×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13101723, #13101727, #13101759, … |
| maximal normal subgroup of | #13101723, #13101727, #13101759, … |
| maximal quotient of | C2×#11717210, C2×#11717212, C2×#11717213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1178);