Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#87764 |
| derived, Sylow | C52 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #1043 |
| commutator, hypocenter | C52 | C22×C16 |
| Frattini | C4 | C22×#1043 |
| Fitting | C22×C4×C52 | C4 |
| socle, prime radical | C23×C52 | C8 |
| cosocle | #6029 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C4 | |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7106);