Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×#1043 |
| Fitting | C42×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #1043 |
| commutator, hypocenter | C52 | C43 |
| Frattini | C22 | C22×#1043 |
| Fitting | C42×C52 | C4 |
| socle | C22×C52 | C22×C4 |
| prime radical, cosocle | C22×C5⋊D5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C42 | |
1032 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #127×#1043, #72213321, #97×#1043, … |
| maximal normal subgroup of | #127×#1043, #72213321, #97×#1043, … |
| maximal quotient of | #97×#1043, C4×C8×#1043, C4×#11716860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7049);