Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6053 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#6053 |
| Fitting | C52×C8 ⋊ C8 |
| derived, Sylow | C52 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #6053 |
| commutator, hypocenter | C52 | C82 |
| Frattini | C4 | C2×#6053 |
| Fitting | C52×C8 | C8 |
| socle | C2×C52 | C4×C8 |
| prime radical | C2×C5⋊D5 | C42 |
| cosocle | C4×#1043 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C8 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C8×AGL(1,𝔽25), C3×C8×#6053 |
| maximal normal subgroup of | C8×AGL(1,𝔽25), C3×C8×#6053 |
| maximal quotient of | C3×C8×#6053 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5748);