Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D52 |
| unambiguous semidirect product | (C5×D5)⋊C24 |
| unambiguous semidirect product | (C5⋊D5)⋊C24 |
| Fitting, socle | C23×C52 ⋊ C22 |
| derived, Sylow | C52 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D52 |
| commutator, cosocle, hypocenter | C52 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C52 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23 | |
1630 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13101580, #13103801, #13104117, … |
| maximal normal subgroup of | #13101580, #13103801, #13104117, … |
| maximal quotient of | C22×D5×Dic10, C22×#87870, C22×#87871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1208);