Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#87707 |
| derived, Sylow | C25 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D25 |
| commutator, hypocenter | C25 | C2×C16 |
| Frattini | C5×C8 | C2×D5 |
| Fitting | C2×C8×C25 | C2 |
| socle, prime radical | C22×C5 | #168 |
| cosocle | C8×C25 | C22 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C8 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#87707, #13097665, C4⋊#87707, … |
| maximal normal subgroup of | C4×#87707, #13097665, C4⋊#87707, … |
| maximal quotient of | C4×#87707, C4⋊#87707, C2×#11716342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 18);