Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C42×C5×D5 |
| Fitting | C2×C42×C52 ⋊ C2 |
| derived | C5 ⋊ C22×C42×C5 |
| Sylow | C52 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42×C5 | D5 |
| commutator, hypocenter | C5 | C22×C42×C5 |
| Frattini | C22 | C23×C5×D5 |
| Fitting | C2×C42×C52 | C2 |
| socle | C23×C52 | C23 |
| prime radical | C23×C5×D5 | C22 |
| cosocle | C22×C5 | C24×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C42×C5 | |
1104 conjugacy classes of subgroups; only the 606 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 606 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C42×D52, C2×C5×D5×#127, C2×D5×#4020 |
| maximal normal subgroup of | C2×C42×D52, C2×C5×D5×#127, C2×D5×#4020 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8977);