Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C52 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#6053 |
| commutator, socle | C2×C52 | C2×C16 |
| Fitting | C2×C4×C52 | C8 |
| prime radical | C22×C52 | C16 |
| cosocle | #87764 | C22 |
| hypercenter | C2×C4 | #6053 |
| hypocenter | C52 | M64 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=h,h^a=g^2,g^c=g^2,h^c=h^2,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, 5757);