Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#6014 |
| derived, Sylow | C25 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D25 |
| commutator, hypocenter | C25 | C4×C8 |
| Frattini | C2×C4×C5 | C2×D5 |
| Fitting | C42×C25 | C2 |
| socle, prime radical | C22×C5 | C2×Dic5 |
| cosocle | C2×C4×C25 | C22 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C42 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#6014, #13097660, #13097661, … |
| maximal normal subgroup of | C8×#6014, #13097660, #13097661, … |
| maximal quotient of | C8×#6014, #13097661, C4×#87707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 9);