Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×Dic52 |
| derived, Sylow | C52 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D52 |
| commutator, hypocenter | C52 | C2×C42 |
| Frattini | C22 | C2×D52 |
| Fitting, socle, prime radical | C23×C52 | C22 |
| cosocle | C22×C52 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23 | |
270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13099832, #13099933, #13100006, … |
| maximal normal subgroup of | #13099832, #13099933, #13100006, … |
| maximal quotient of | #13101234, C2×Dic5×#168, Dic5×#681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 731);