Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C16×#1043 |
| Fitting | C52×C16 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #1043 |
| commutator, hypocenter | C52 | C4×C16 |
| Frattini | C8 | C2×#1043 |
| Fitting | C52×C16 | C4 |
| socle | C2×C52 | C4×C8 |
| prime radical | C2×C5⋊D5 | C2×C8 |
| cosocle | C8×C5⋊D5 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C16 | |
232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C16×#1043, M32×#1043, D16×#1043, … |
| maximal normal subgroup of | C2×C16×#1043, M32×#1043, D16×#1043, … |
| maximal quotient of | C2×C16×#1043, #1043×AGL(1,𝔽17) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2573);