Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43×C5 |
| direct product | C42×#1044 |
| Fitting | C42×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #1044 |
| commutator, hypocenter | C52 | C43 |
| Frattini | C22 | C22×#1044 |
| Fitting | C42×C52 | C4 |
| socle | C22×C52 | C22×C4 |
| prime radical, cosocle | C22×C5⋊D5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C42 | |
624 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C42×D5⋊AGL(1,𝔽5), #127×#1044, #72221574, … |
| maximal normal subgroup of | C42×D5⋊AGL(1,𝔽5), #127×#1044, #72221574, … |
| maximal quotient of | C2×C42×#1044 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7175);