Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of (D5⋊AGL(1,𝔽5))⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×(D5⋊AGL(1,𝔽5))⋊C2 |
| unambiguous semidirect product | (D5⋊AGL(1,𝔽5))⋊C22 |
| unambiguous semidirect product | (D52⋊C2)⋊C22 |
| unambiguous semidirect product | #6057⋊C22 |
| Fitting, socle | C2×C52 ⋊ #41 |
| Sylow | C52 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (D5⋊AGL(1,𝔽5))⋊C2 |
| commutator, cosocle | C5⋊D5 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52 | #41 |
| hypocenter | C52 | C2×#41 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C2 | |
245 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20 |
32 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(D5⋊AGL(1,𝔽5))⋊C2, #13107496, #13107497, … |
| maximal normal subgroup of | C4×(D5⋊AGL(1,𝔽5))⋊C2, #13107496, #13107497, … |
| maximal quotient of | (D5⋊AGL(1,𝔽5))⋊Q8, #13107482, #13107483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1194);