Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6053 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #6053 |
| commutator, hypocenter | C52 | C64 |
| Fitting | C52×C8 | C8 |
| socle, prime radical | C2×C52 | C32 |
| cosocle | #11716580 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C8 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^6,5^2|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=h,h^a=g^2,g^b=g^2,h^b=h^2,g^c=g^4,h^c=h^488 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2061);