Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6037 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#87873 |
| Sylow | C52 ⋊ C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D52 |
| commutator | C2×C52 | C23×C4 |
| Frattini | C22 | C22×D52 |
| Fitting | C42×C52 | C22 |
| socle, cosocle | C22×C52 | C24 |
| prime radical | C2×#87873 | C2 |
| hypocenter | C52 | C4×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C42 | |
728 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11717471, #72258485 |
| maximal normal subgroup of | C4×#11717471, #72258485 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7385);