Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#6033 |
| derived, Sylow | C52 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #1043 |
| commutator, hypocenter | C52 | C82 |
| Frattini | C2×C4 | C2×#1043 |
| Fitting | C2×C52×C8 | C4 |
| socle, prime radical | C22×C52 | C42 |
| cosocle | C4×#1039 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C8 | |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#87855, #72221170, #72221172, … |
| maximal normal subgroup of | C8×#87855, #72221170, #72221172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2608);