Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C5 |
| direct product | C24×C5⋊D5 |
| Fitting, socle | C24×C52 ⋊ C2 |
| derived, Sylow | C52 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C52 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C24 | |
2992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #13101890, #13102819, #13104812, … |
| maximal normal subgroup of | #13101890, #13102819, #13104812, … |
| maximal quotient of | C23×#6045, C23×C4×C5⋊D5, C23×C4⋊(C5⋊D5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1210);