Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D52 |
| commutator, hypocenter | C52 | C2×C32 |
| Fitting, cosocle | C52×C16 | C22 |
| socle | C2×C52 | C2×C16 |
| prime radical | C2×C5⋊D5 | C16 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C16 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=c,c^2=d,d^2=e,e^2=f,h^a=h^4,g^b=g^4256 conjugacy classes — view the full character table.
| maximal subgroup of | #72269143, #72269157, #72269158 |
| maximal normal subgroup of | #72269143, #72269157, #72269158 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1589);