Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×#6036 |
| derived, Sylow | C52 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D52 |
| commutator, hypocenter | C52 | C22×C42 |
| Frattini | C22 | C22×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C23×C52 | C23 |
| prime radical | C23×C5⋊D5 | C22 |
| cosocle | C22×C52 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C4 | |
1232 conjugacy classes of subgroups; only the 384 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 384 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13105369, C2×#13103998, C2×#13106199, … |
| maximal normal subgroup of | C2×#13105369, C2×#13103998, C2×#13106199, … |
| maximal quotient of | C4×#11716936, C2×#13100501, C22×C4×#6036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8289);