Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×#11716581 |
| derived, Sylow | C52 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #1044 |
| commutator, hypocenter | C52 | C2×C32 |
| Frattini | C8 | C2×#1044 |
| Fitting | C2×C52×C8 | C4 |
| socle, prime radical | C22×C52 | C16 |
| cosocle | #87756 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C8 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2698);