Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D5⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊(D5⋊C16) |
| derived, Sylow | C52 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C22×C16 |
| Frattini | C4 | C2×D5⋊AGL(1,𝔽5) |
| Fitting | C52×C8 | C2×C4 |
| socle | C2×C52 | C22×C8 |
| prime radical | C2×D52 | C8 |
| cosocle | #6029 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C8 | |
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=e,c^2=e,d^2=e,e^2=f,g^a=g^2,h^a=h^2,g^b=g^4,g^d=g^4,h^d=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | C16×D5⋊AGL(1,𝔽5), #72244825 |
| maximal normal subgroup of | C16×D5⋊AGL(1,𝔽5) |
| maximal quotient of | #72244825 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6188);