Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D52⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D52⋊C2 |
| commutator | C5⋊D5 | C2×C16 |
| Fitting | C52×C8 | D4 |
| socle | C2×C52 | C4⋊C8 |
| prime radical | C2×C5⋊D5 | C2×C8 |
| cosocle | C8×C5⋊D5 | C22 |
| hypocenter | C52 | C4⋊C16 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C8 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=d,c^2=f,d^2=e,e^2=f,b^a=bcef,g^a=g^2,h^a=h^3,g^b=h^4,h^b=g^4,g^c=g^4,h^c=h^4112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2306);