Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of (D5⋊AGL(1,𝔽5))⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C52 ⋊ #431 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | (D5⋊AGL(1,𝔽5))⋊C2 |
| commutator | C5⋊D5 | C22×C8 |
| Fitting | C4×C52 | #41 |
| socle | C2×C52 | #117 |
| prime radical | C2×D52 | C2×C4 |
| cosocle | C4×C5⋊D5 | C23 |
| hypocenter | C52 | #431 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C4 | |
216 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^6,5^2|b^2=d,c^2=e,e^2=f,c^a=cdf,g^a=g^4,c^b=cdf,g^b=g^2,h^b=h^3,g^c=h^4,h^c=g^4,g^d=g^4,h^d=h^464 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5658);