Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #41×D25 |
| Fitting | #41×C25 ⋊ C2 |
| Sylow | C25 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D25 |
| commutator, cosocle | C2×C25 | C24 |
| Frattini, socle | C2×C5 | C23×D5 |
| Fitting | #41×C25 | C2 |
| hypercenter | #41 | D25 |
| hypocenter | C25 | C2×#41 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C4 ◁ #41 | |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #104×D25, #13098096, D25⋊#104, … |
| maximal normal subgroup of | #104×D25, #13098096, D25⋊#104, … |
| maximal quotient of | #13098840, #13098841, #13098842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 226);