Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D52×M16 |
| Fitting | C52×M16 ⋊ C22 |
| Sylow | C52 ⋊ C22×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D52 |
| commutator, socle | C2×C52 | C23×C4 |
| Fitting | C52×M16 | C22 |
| prime radical | C22×D52 | C4 |
| cosocle | C4×C52 | C24 |
| hypercenter | M16 | D52 |
| hypocenter | C52 | C22×M16 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ M16 | |
664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | M16×D5⋊AGL(1,𝔽5), #72220837, #72220838, … |
| maximal normal subgroup of | M16×D5⋊AGL(1,𝔽5), #72220837, #72220838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8147);